Convex Model-Based Reduced-Order Model for Uncertain Control Systems

This study proposes a convex model-based reduced-order model (CMBROM) method for uncertain linear control systems, which ensures the accuracy of the reduced-order model with small samplings. Once the convex bounds of uncertainties are known, the coefficient matrices, input, and output in the uncertain state-space equation are quantified as convex model-based (CMB) parameters. A novel CMB state-space equation is constituted based on an order-extended matrix, which can solve the deterministic and uncertain parts of the state and output using the proposed solution method. The controllability and stability of the CMB state-space system have been proved. The conventional balance system is extended into a convex model format as an important fundamental process for order reduction, and the nominal and uncertain balanced coefficient matrices can be obtained using the transformation matrix. By solving the uncertain controllable and observability matrices using the CMB Lyapunov equation, a convex model perturbation-based singular value decomposition (SVD) is proposed to estimate the uncertain Hankel singular values. Finally, the CMB order-truncated criterion is set using the CMB possibility.