Matrix Equation $XA + BX = C$

Previous article Next article Matrix Equation $XA + BX = C$R. A. SmithR. A. Smithhttps://doi.org/10.1137/0116017PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. Barnett and , C. Storey, Some applications of the Lyapunov matrix equation, J. Inst. Math. Appl., to appear Google Scholar[2] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar[3] W. G. Bickley and , J. McNamee, Matrix and other direct methods for the solution of systems of linear difference equations, Philos. Trans. Rov. Soc. London Ser. A, 252 (1960), 69–131 MR0114067 0092.13001 CrossrefISIGoogle Scholar[4] Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964xi+257 MR0175290 0161.12101 Google Scholar[5] Er-chieh Ma, A finite series solution of the matrix equation $AX-XB=C$, SIAM J. Appl. Math., 14 (1966), 490–495 10.1137/0114043 MR0201456 0144.27003 LinkISIGoogle Scholar[6] D. E. Rutherford, On the solution of the matrix equation $AX+XB=C$, Nederl. Akad. Wetensch. Proc. Ser. A, 35 (1932), 53–59 0004.19502 Google Scholar[7] R. A. Smith, Bounds for quadratic Lyapunov functions, J. Math. Anal. Appl., 12 (1965), 425–435 10.1016/0022-247X(65)90010-7 MR0190475 0135.29802 CrossrefISIGoogle Scholar[8] R. A. Smith, Matrix calculations for Liapunov quadratic forms, J. Differential Equations, 2 (1966), 208–217 10.1016/0022-0396(66)90044-1 MR0188557 0151.02206 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Iterative Approach for Reduction of Index-2 Periodic Models Using Generalized Inverse ProcedureProceedings of Seventh International Congress on Information and Communication Technology | 3 August 2022 Cross Ref Combined real and imaginary parts method for solving generalized Lyapunov matrix equationApplied Numerical Mathematics, Vol. 181 | 1 Nov 2022 Cross Ref Balanced truncation for discrete time-delay systems via the interpretation of system energyJournal of the Franklin Institute, Vol. 359, No. 15 | 1 Oct 2022 Cross Ref New results of the IO iteration algorithm for solving Sylvester matrix equationJournal of the Franklin Institute, Vol. 359, No. 15 | 1 Oct 2022 Cross Ref Developing Kaczmarz method for solving Sylvester matrix equationsJournal of the Franklin Institute, Vol. 35 | 1 Sep 2022 Cross Ref Label driven latent subspace learning for multi-view multi-label classificationApplied Intelligence, Vol. 37 | 3 June 2022 Cross Ref A new approximation algorithm for solving generalized Lyapunov matrix equationsJournal of Computational and Applied Mathematics, Vol. 404 | 1 Apr 2022 Cross Ref On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equationsComputers & Mathematics with Applications, Vol. 109 | 1 Mar 2022 Cross Ref Data-Driven Balancing of Linear Dynamical SystemsIon Victor Gosea, Serkan Gugercin, and Christopher BeattieSIAM Journal on Scientific Computing, Vol. 44, No. 1 | 28 February 2022AbstractPDF (1090 KB)Solving Sylvester equation with complex symmetric semi-definite positive coefficient matricesFilomat, Vol. 36, No. 5 | 1 Jan 2022 Cross Ref Learnable low-rank latent dictionary for subspace clusteringPattern Recognition, Vol. 120 | 1 Dec 2021 Cross Ref A dual reduction strategy for reduce-order modeling of periodic control systemResults in Control and Optimization, Vol. 4 | 1 Sep 2021 Cross Ref A comparison of numerical methods for model reduction of dense discrete-time systemsat - Automatisierungstechnik, Vol. 69, No. 8 | 10 August 2021 Cross Ref Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systemsLinear Algebra and its Applications, Vol. 623 | 1 Aug 2021 Cross Ref Hermitian and skew-Hermitian splitting methods for solving a tensor equationInternational Journal of Computer Mathematics, Vol. 98, No. 6 | 9 September 2020 Cross Ref Modified Iterations for Data-Sparse Solution of Linear SystemsVietnam Journal of Mathematics, Vol. 49, No. 2 | 5 May 2021 Cross Ref An extension method for fully fuzzy Sylvester matrix equationSoft Computing, Vol. 25, No. 7 | 13 January 2021 Cross Ref A relaxed MSIO iteration algorithm for solving coupled discrete Markovian jump Lyapunov equationsJournal of the Franklin Institute, Vol. 358, No. 6 | 1 Apr 2021 Cross Ref Solving large-scale nonsymmetric algebraic Riccati equations from two-dimensional transport models by doublingJournal of Computational and Applied Mathematics, Vol. 23 | 1 Feb 2021 Cross Ref A structured Krylov subspace approach based model reduction of periodic control system in lifted form2021 6th International Conference on Inventive Computation Technologies (ICICT) | 20 Jan 2021 Cross Ref Solving complex Sylvester matrix equation by accelerated double-step scale splitting (ADSS) methodEngineering with Computers, Vol. 37, No. 1 | 27 August 2019 Cross Ref Iterative and doubling algorithms for Riccati‐type matrix equations: A comparative introductionGAMM-Mitteilungen, Vol. 43, No. 4 | 8 October 2020 Cross Ref On inexact alternating direction implicit iteration for continuous Sylvester equationsNumerical Linear Algebra with Applications, Vol. 27, No. 5 | 20 July 2020 Cross Ref On the semigroup property for some structured iterationsJournal of Computational and Applied Mathematics, Vol. 374 | 1 Aug 2020 Cross Ref A multi-step Smith-inner-outer iteration algorithm for solving coupled continuous Markovian jump Lyapunov matrix equationsJournal of the Franklin Institute, Vol. 357, No. 6 | 1 Apr 2020 Cross Ref Optimal Linear-Quadratic Controller DesignController Design for Distributed Parameter Systems | 2 June 2020 Cross Ref An efficient algorithm for reduce order modeling of discrete-time index-2 descriptor control systems2019 22nd International Conference on Computer and Information Technology (ICCIT) | 1 Dec 2019 Cross Ref Residual-based iterations for the generalized Lyapunov equationBIT Numerical Mathematics, Vol. 59, No. 4 | 15 June 2019 Cross Ref Distributed optimisation design for solving the Stein equation with constraintsIET Control Theory & Applications, Vol. 13, No. 15 | 1 August 2019 Cross Ref The double-step scale splitting method for solving complex Sylvester matrix equationComputational and Applied Mathematics, Vol. 38, No. 3 | 5 August 2019 Cross Ref A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equationApplied Mathematics and Computation, Vol. 348 | 1 May 2019 Cross Ref An efficient model reduction strategy for discrete-time index-2 descriptor control systems2019 International Conference on Electrical, Computer and Communication Engineering (ECCE) | 1 Feb 2019 Cross Ref New explicit iteration algorithms for solving coupled continuous Markovian jump Lyapunov matrix equationsJournal of the Franklin Institute, Vol. 355, No. 17 | 1 Nov 2018 Cross Ref The solution of fuzzy Sylvester matrix equationSoft Computing, Vol. 22, No. 19 | 21 July 2017 Cross Ref K-cyclic Smith iterative method for model reduction of index-2 periodic control systems2018 International Conference on Innovations in Science, Engineering and Technology (ICISET) | 1 Oct 2018 Cross Ref On the singular values of matrices with high displacement rankLinear Algebra and its Applications, Vol. 548 | 1 Jul 2018 Cross Ref An improved particle filtering-based approach for health prediction and prognosis of nonlinear systemsJournal of the Franklin Institute, Vol. 355, No. 8 | 1 May 2018 Cross Ref Object Classification With Joint Projection and Low-Rank Dictionary LearningIEEE Transactions on Image Processing, Vol. 27, No. 2 | 1 Feb 2018 Cross Ref Preconditioned HSS iteration method and its non-alternating variant for continuous Sylvester equationsComputers & Mathematics with Applications, Vol. 75, No. 4 | 1 Feb 2018 Cross Ref Spectral decomposition based solutions to the matrix equationIET Control Theory & Applications, Vol. 12, No. 1 | 1 January 2018 Cross Ref Structure preserving iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systemsNumerical Algorithms, Vol. 76, No. 4 | 23 February 2017 Cross Ref A Parallel Two-Stage Iteration Method for Solving Continuous Sylvester EquationsAlgorithms, Vol. 10, No. 3 | 21 August 2017 Cross Ref GRADIENT BASED ITERATIVE ALGORITHM TO SOLVE GENERAL COUPLED DISCRETE-TIME PERIODIC MATRIX EQUATIONS OVER GENERALIZED REFLEXIVE MATRICESMathematical Modelling and Analysis, Vol. 21, No. 4 | 23 June 2016 Cross Ref A note on the Davison–Man method for Sylvester matrix equationsComputational and Applied Mathematics, Vol. 36, No. 1 | 5 June 2015 Cross Ref Efficient Techniques for Solving the Periodic Projected Lyapunov Equations and Model Reduction of Periodic SystemsMathematical Problems in Engineering, Vol. 2017 | 1 Jan 2017 Cross Ref An implicitly restarted rational Krylov strategy for Lyapunov inverse iterationIMA Journal of Numerical Analysis, Vol. 36, No. 2 | 18 May 2015 Cross Ref A new linearized implicit iteration method for nonsymmetric algebraic Riccati equationsJournal of Applied Mathematics and Computing, Vol. 50, No. 1-2 | 3 February 2015 Cross Ref Multi-view low-rank dictionary learning for image classificationPattern Recognition, Vol. 50 | 1 Feb 2016 Cross Ref Computational Methods for Linear Matrix EquationsV. SimonciniSIAM Review, Vol. 58, No. 3 | 4 August 2016AbstractPDF (851 KB)A Parameter Free ADI-Like Method for the Numerical Solution of Large Scale Lyapunov EquationsSplitting Methods in Communication, Imaging, Science, and Engineering | 6 January 2017 Cross Ref On the NPHSS-KPIK iteration method for low-rank complex Sylvester equations arising from time-periodic fractional diffusion equationsTURKISH JOURNAL OF MATHEMATICS, Vol. 40 | 1 Jan 2016 Cross Ref A NEW VERSION OF THE SMITH METHOD FOR SOLVING SYLVESTER EQUATION AND DISCRETE-TIME SYLVESTER EQUATIONJournal of Applied Analysis & Computation, Vol. 6, No. 2 | 1 Jan 2016 Cross Ref A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equationsApplied Mathematics and Computation, Vol. 271 | 1 Nov 2015 Cross Ref On modified HSS iteration methods for continuous Sylvester equationsApplied Mathematics and Computation, Vol. 263 | 1 Jul 2015 Cross Ref A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical SystemsPeter Benner, Serkan Gugercin, and Karen WillcoxSIAM Review, Vol. 57, No. 4 | 5 November 2015AbstractPDF (426 KB)A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix EquationsCircuits, Systems, and Signal Processing, Vol. 34, No. 1 | 1 July 2014 Cross Ref Matrix polynomial and epsilon-type extrapolation methods with applicationsNumerical Algorithms, Vol. 68, No. 1 | 14 June 2014 Cross Ref Low-rank iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systemsNumerical Algorithms, Vol. 67, No. 3 | 11 January 2014 Cross Ref On normal and skew-Hermitian splitting iteration methods for large sparse continuous Sylvester equationsJournal of Computational and Applied Mathematics, Vol. 268 | 1 Oct 2014 Cross Ref On the squared Smith method for large-scale Stein equationsNumerical Linear Algebra with Applications, Vol. 21, No. 5 | 12 December 2013 Cross Ref Extended Hamiltonian algorithm for the solution of discrete algebraic Lyapunov equationsApplied Mathematics and Computation, Vol. 234 | 1 May 2014 Cross Ref On inexact Newton methods based on doubling iteration scheme for symmetric algebraic Riccati equationsJournal of Computational and Applied Mathematics, Vol. 260 | 1 Apr 2014 Cross Ref Generalized inverses of periodic matrix pairs and model reduction for periodic control systems2014 International Conference on Electrical Engineering and Information & Communication Technology | 1 Apr 2014 Cross Ref The Simplified Topological $\varepsilon$-Algorithms for Accelerating Sequences in a Vector SpaceClaude Brezinski and Michela Redivo-ZagliaSIAM Journal on Scientific Computing, Vol. 36, No. 5 | 23 September 2014AbstractPDF (328 KB)Numerical MethodsApplied Dynamics | 27 June 2014 Cross Ref A Generalized HSS Iteration Method for Continuous Sylvester EquationsJournal of Applied Mathematics, Vol. 2014 | 1 Jan 2014 Cross Ref Ride Comfort and Road HoldingRoad and Off-Road Vehicle System Dynamics Handbook | 30 October 2013 Cross Ref On the convergence of inexact Newton methods for discrete-time algebraic Riccati equationsLinear Algebra and its Applications, Vol. 439, No. 7 | 1 Oct 2013 Cross Ref Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art surveyGAMM-Mitteilungen, Vol. 36, No. 1 | 13 August 2013 Cross Ref Large-scale Stein and Lyapunov equations, Smith method, and applicationsNumerical Algorithms, Vol. 63, No. 4 | 13 October 2012 Cross Ref A preconditioned block Arnoldi method for large Sylvester matrix equationsNumerical Linear Algebra with Applications, Vol. 20, No. 2 | 7 December 2011 Cross Ref Finite-Rank ADI Iteration for Operator Lyapunov EquationsMark R. Opmeer, Timo Reis, and Winnifried WollnerSIAM Journal on Control and Optimization, Vol. 51, No. 5 | 28 October 2013AbstractPDF (419 KB)Model Problems and PreconditioningThe ADI Model Problem | 8 March 2013 Cross Ref An Alternating Direction Implicit Method for Solving Projected Generalized Continuous-Time Sylvester EquationsMathematical Problems in Engineering, Vol. 2013 | 1 Jan 2013 Cross Ref A Note on the ⊤ -Stein Matrix EquationAbstract and Applied Analysis, Vol. 2013 | 1 Jan 2013 Cross Ref Iterative solvers for periodic matrix equations and model reduction for periodic control systems2012 7th International Conference on Electrical and Computer Engineering | 1 Dec 2012 Cross Ref Computational Hydrodynamic Stability and Flow Control Based on Spectral Analysis of Linear OperatorsArchives of Computational Methods in Engineering, Vol. 19, No. 3 | 2 August 2012 Cross Ref Development, Implementation, and Application of an Analytic Second Derivative Formalism for the Normalized Elimination of the Small Component MethodJournal of Chemical Theory and Computation, Vol. 8, No. 8 | 10 July 2012 Cross Ref An improved algorithm for balanced POD through an analytic treatment of impulse response tailsJournal of Computational Physics, Vol. 231, No. 16 | 1 Jun 2012 Cross Ref Accurate solutions of M-matrix Sylvester equationsNumerische Mathematik, Vol. 120, No. 4 | 12 October 2011 Cross Ref Accurate solutions of M-matrix algebraic Riccati equationsNumerische Mathematik, Vol. 120, No. 4 | 12 October 2011 Cross Ref A reflection on the implicitly restarted Arnoldi method for computing eigenvalues near a vertical lineLinear Algebra and its Applications, Vol. 436, No. 8 | 1 Apr 2012 Cross Ref A low-rank Krylov squared Smith method for large-scale discrete-time Lyapunov equationsLinear Algebra and its Applications, Vol. 436, No. 8 | 1 Apr 2012 Cross Ref Alternating-directional Doubling Algorithm for M-Matrix Algebraic Riccati EquationsWei-guo Wang, Wei-chao Wang, and Ren-Cang LiSIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 1 | 8 March 2012AbstractPDF (372 KB)Deterministic Continuation of Stochastic Metastable Equilibria via Lyapunov Equations and EllipsoidsChristian KuehnSIAM Journal on Scientific Computing, Vol. 34, No. 3 | 19 June 2012AbstractPDF (916 KB)Structure Preserving Iterative Solution of Periodic Projected Lyapunov EquationsIFAC Proceedings Volumes, Vol. 45, No. 2 | 1 Jan 2012 Cross Ref On the numerical solution of large-scale sparse discrete-time Riccati equationsAdvances in Computational Mathematics, Vol. 35, No. 2-4 | 4 August 2011 Cross Ref Toward solution of matrix equation X=Af(X)B+CLinear Algebra and its Applications, Vol. 435, No. 6 | 1 Sep 2011 Cross Ref On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equationsNumerical Linear Algebra with Applications, Vol. 18, No. 3 | 13 April 2011 Cross Ref Distributed Control in Multiple Dimensions: A Structure Preserving Computational TechniqueIEEE Transactions on Automatic Control, Vol. 56, No. 3 | 1 Mar 2011 Cross Ref Model Reduction of Periodic Descriptor Systems Using Balanced TruncationModel Reduction for Circuit Simulation | 25 March 2011 Cross Ref A Computational Method for Symmetric Stein Matrix EquationsNumerical Linear Algebra in Signals, Systems and Control | 22 May 2011 Cross Ref Iterative solutions to the Kalman–Yakubovich-conjugate matrix equationApplied Mathematics and Computation, Vol. 217, No. 9 | 1 Jan 2011 Cross Ref Approximation of low rank solutions for linear quadratic control of partial differential equationsComputational Optimization and Applications, Vol. 46, No. 1 | 12 July 2008 Cross Ref ADI preconditioned Krylov methods for large Lyapunov matrix equationsLinear Algebra and its Applications, Vol. 432, No. 10 | 1 May 2010 Cross Ref An efficient algorithm for solving general coupled matrix equations and its applicationMathematical and Computer Modelling, Vol. 51, No. 9-10 | 1 May 2010 Cross Ref Analysis of the solution of the Sylvester equation using low-rank ADI with exact shiftsSystems & Control Letters, Vol. 59, No. 3-4 | 1 Mar 2010 Cross Ref Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale ProblemsKarl Meerbergen and Alastair SpenceSIAM Journal on Matrix Analysis and Applications, Vol. 31, No. 4 | 7 May 2010AbstractPDF (281 KB)On Smith-type iterative algorithms for the Stein matrix equationApplied Mathematics Letters, Vol. 22, No. 7 | 1 Jul 2009 Cross Ref Inexact Kleinman–Newton Method for Riccati EquationsF. Feitzinger, T. Hylla, and E. W. SachsSIAM Journal on Matrix Analysis and Applications, Vol. 31, No. 2 | 18 March 2009AbstractPDF (222 KB)Vehicle and Guideway Modelling: Suspensions SystemsDynamical Analysis of Vehicle Systems | 1 Jan 2009 Cross Ref Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problemsNumerical Linear Algebra with Applications, Vol. 15, No. 9 | 1 Nov 2008 Cross Ref Trail to a Lyapunov equation solverComputers & Mathematics with Applications, Vol. 55, No. 8 | 1 Apr 2008 Cross Ref Gramian-Based Model Reduction for Data-Sparse SystemsUlrike Baur and Peter BennerSIAM Journal on Scientific Computing, Vol. 31, No. 1 | 12 November 2008AbstractPDF (346 KB)Factorized Solution of Lyapunov Equations Based on Hierarchical Matrix ArithmeticComputing, Vol. 78, No. 3 | 9 November 2006 Cross Ref White noise excitation of road vehicle structuresSadhana, Vol. 31, No. 4 | 1 Aug 2006 Cross Ref Algorithms for model reduction of large dynamical systemsLinear Algebra and its Applications, Vol. 415, No. 2-3 | 1 Jun 2006 Cross Ref Iterative Solution of Algebraic Riccati Equations for Damped SystemsProceedings of the 45th IEEE Conference on Decision and Control | 1 Jan 2006 Cross Ref Model-order reduction by dominant subspace projection: error bound, subspace computation, and circuit applicationsIEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 52, No. 5 | 1 May 2005 Cross Ref Parallel algorithms for model reduction of discrete-time systemsInternational Journal of Systems Science, Vol. 34, No. 5 | 1 Apr 2003 Cross Ref Remote Parallel Model Reduction of Linear Time-Invariant Systems Made EasyHigh Performance Computing for Computational Science — VECPAR 2002 | 15 April 2003 Cross Ref NUMERICAL SOLUTION OF DISCRETE STABLE LINEAR MATRIX EQUATIONS ON MULTICOMPUTERSParallel Algorithms and Applications, Vol. 17, No. 2 | 1 Jan 2002 Cross Ref A factorization-based framework for passivity-preserving model reduction of RLC systemsProceedings 2002 Design Automation Conference (IEEE Cat. No.02CH37324) | 1 Jan 2002 Cross Ref Specialized Parallel Algorithms for Solving Lyapunov and Stein EquationsJournal of Parallel and Distributed Computing, Vol. 61, No. 10 | 1 Oct 2001 Cross Ref Parallel solvers for discrete-time algebric Riccati equationsConcurrency and Computation: Practice and Experience, Vol. 13, No. 2 | 27 February 2001 Cross Ref Efficient balance-and-truncate model reduction for large scale systemsProceedings of the 2001 American Control Conference. (Cat. No.01CH37148) | 1 Jan 2001 Cross Ref Parallel solutions of very large sparse Lyapunov equations by balanced BBD decompositionsIEEE Transactions on Automatic Control, Vol. 44, No. 3 | 1 Mar 1999 Cross Ref A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov EquationsThilo PenzlSIAM Journal on Scientific Computing, Vol. 21, No. 4 | 25 July 2006AbstractPDF (377 KB)Solving Stable Stein Equations on Distributed Memory Parallel | 6 August 1999 Cross Ref Alternating direction algorithms for solving equationsApplied Mathematics & Optimization, Vol. 34, No. 3 | 1 Nov Cross Ref Solving the linear quadratic optimal control for & Mathematics with Applications, Vol. No. 9 | 1 Nov Cross Ref method and the high tensor equation Mathematics and Vol. 17, No. 10 | 1 Oct Cross Ref The linear tensor equation Mathematics and Vol. 17, No. 10 | 1 Oct Cross Ref Preconditioned Krylov Methods for Lyapunov Matrix and Journal on Matrix Analysis and Applications, Vol. No. 1 | 17 July 2006AbstractPDF Matrix Equation in System Stability and Control | 1 Jan Cross Ref Continuous algebraic Lyapunov Matrix Equation in System Stability and Control | 1 Jan Cross Ref algebraic Lyapunov Matrix Equation in System Stability and Control | 1 Jan Cross Ref Iterative methods and Matrix Equation in System Stability and Control | 1 Jan Cross Ref The method for - = Journal of Computer Mathematics, Vol. 52, No. 1-2 | 1 Jan Cross Ref of and of a Matrix Riccati Journal on Analysis, Vol. No. 6 | 17 July 2006AbstractPDF KB)A preconditioned method for + = Journal of Computer Mathematics, Vol. 49, No. 3-4 | 1 Jan Cross Ref bounds for matrix and Algebra and its Applications, Vol. | 1 Sep Cross Ref and the tensor equation of Vol. 27, No. 3 | 1 Mar Cross Ref for Algebra and its Applications, Vol. | 1 Aug Cross Ref Alternating Direction Implicit Iteration for Systems with S. and Journal on Numerical Analysis, Vol. No. 3 | 14 July 2006AbstractPDF KB)A Numerical Algorithm for Optimal in Linear T. and Journal on Control and Optimization, Vol. No. 3 | 14 July 2006AbstractPDF KB)On the of the equations and in a a Journal of Mathematics, Vol. 20, No. 2 | 1 Jun Cross Ref Computational and of some Riccati equation of Control, and Vol. 12, No. 4 | 1 Jul Cross Ref The iterative solution of the matrix equation + BX + = Algebra and its Applications, Vol. | 1 Jul Cross Ref Iterative solution of the Lyapunov matrix equationApplied Mathematics Letters, Vol. No. 1 | 1 Jan Cross Ref Approximation for Systems and the Riccati and D. Journal on Control and Optimization, Vol. 25, No. 4 | 14 July 2006AbstractPDF of vehicle Engineering Vol. No. 2 | 1 Jun Cross Ref On the of linear Transactions on Circuits and Systems, Vol. 33, No. 5 | 1 May Cross Ref in control of the of and Control, Vol. No. 5 | 2 July 2016 Cross Ref The An design in Vol. 6, No. 1 | 1 Feb Cross Ref and Applied | 1 Jan Cross Ref for of the control system in in Automatic Vol. 12 | 1 Jan Cross Ref A of methods in Engineering and Vol. No. 3 | 1 Jun Cross Ref A Computer Design Proceedings Volumes, Vol. No. 19 | 1 Sep Cross Ref A Design of Systems | 1 Jan Cross Ref on model reduction by the equation Transactions on Automatic Control, Vol. 27, No. 4 | 1 Aug Cross Ref and control scheme state Control and Vol. No. 1 | October Cross Ref and Control System Design of of | 1 Jan Cross Ref Vol. 52, No. 1-2 | 1 Jan Cross Ref The of linear discrete-time systems by Journal of Control, Vol. 34, No. 3 | 12 March Cross Ref The of convergence of a matrix Algebra and its Applications, Vol. 35 | 1 Feb Cross Ref An and for differential equations of of the of A Mathematics, Vol. No. 1-2 | 14 November 2011 Cross Ref Vol. 49, No. 3-4 | 1 May Cross Ref A FOR LINEAR Design of Control Systems | 1 Jan Cross Ref ON THE OF TO THE SOLUTION OF of | 1 Jan Cross Ref A for Linear Proceedings Volumes, Vol. 12, No. 7 | 1 Sep Cross Ref On the Application of to the Solution of Optimal Proceedings Volumes, Vol. 12, No. 2 | 1 Sep Cross Ref Analysis of System Vol. 8, No. 2-3 | 27 July Cross Ref Transactions on Automatic Control, Vol. No. 4 | 1 Aug Cross Ref Algorithms for computation of optimal output for linear control and Control Conference | 16 August 2012 Cross Ref An of algorithm for matrix Riccati Vol. No. 2 | 1 Mar Cross Ref solution of matrix Riccati equationInternational Journal of Control, Vol. 27, No. 3 | 19 April Cross Ref The numerical solution = + + = Transactions on Automatic Control, Vol. 22, No. 5 | 1 Oct Cross Ref Optimal approximation of of linear dynamical Transactions on Circuits and Systems, Vol. No. 10 | 1 Oct Cross Ref Design algorithms for a Journal of Control, Vol. 25, No. 6 | 1 Jun Cross Ref in Theory and | 1 Jan Cross Ref A algorithm for linear discrete Transactions on Automatic Control, Vol. 21, No. 4 | 1 Aug Cross Ref Optimal of linear systems with Transactions on Automatic Control, Vol. 21, No. 1 | 1 Feb Cross Ref control theory design IEEE Conference on Decision and Control the on | 1 Dec Cross Ref solutions of the matrix Vol. No. 2-3 | 1 May Cross Ref methods for optimal linear system Journal of Control, Vol. 18, No. 4 | 2 May Cross Ref The of model methods to Journal of Control, Vol. 17, No. 6 | 27 March Cross Ref Analysis of a discrete matrix Riccati equation of linear control and of Analysis and Applications, Vol. No. 1 | 1 Apr Cross Ref Approximation of discrete linear systemsInternational Journal of Control, Vol. 17, No. 3 | 27 March Cross Ref Design of optimal state for large linear Conference on Optimization Techniques | May 2005 Cross Ref A numerical algorithm for the computation of of the IEEE Conference on Decision and Control and on | 1 Dec Cross Ref A Solution of the Matrix Equation + = - Journal on Applied Mathematics, Vol. No. 3 | 12 July 2006AbstractPDF of numerical methods for solving Liapunov matrix Journal of Control, Vol. 15, No. 5 | 1 May Cross Ref Numerical solution of + + = Vol. No. 1 | 1 Jan Cross Ref Numerical solution of the matrix equation + = Transactions on Automatic Control, Vol. No. 3 | 1 Jun Cross Ref Theory of Linear Systems | 1 Jan Cross Ref of Linear Matrix Review, Vol. 12, No. 4 | 18 July 2006AbstractPDF KB)A method for optimal control of a linear system by quadratic Journal of Control, Vol. No. 6 | 16 January Cross Ref Solution of the Matrix Equations + = - and + = - Journal on Applied Mathematics, Vol. 18, No. 3 | 1 August 2006AbstractPDF Methods for Balanced of Large Sparse Reduction of Large-Scale Systems Cross Ref A for solving linear control on on and high computing Cross Ref Efficient balanced truncation of general large-scale RLC systems via Krylov of Design 7th and Design Automation Conference and International Conference on Design Cross Ref A comparison of methods for the general matrix for linear Journal of Control, Vol. 10, No. 6 | 1 Dec Cross Ref Vol. No. | 1 Jun Cross Ref Journal on Applied April July 2006 for and Applied & for and Applied Mathematics