Gain-Scheduled State-Feedback Controllers Using Inexactly Measured Scheduling Parameters: Stabilizing and H∞ Control Problems

This paper tackles two design problems, i.e. stabilizing and H∞ control problems, using Gain-Scheduled (GS) state-feedback controllers for Linear Parameter-Varying (LPV) systems under the condition that the scheduling parameters are inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent state-space matrices and the measured scheduling parameters are supposed to have a priori defined bounded uncertainties. Using parameter-independent Lyapunov functions and parameter-dependent scaling matrices related to the uncertainties in the measured scheduling parameters, we give formulations for designing parametrically affine GS stabilizing and H∞ state-feedback controllers in terms of parametrically affine Linear Matrix Inequalities (LMIs). Our proposed methods encompass the design methods of robust state-feedback controllers as a special case. A simple numerical example for an H∞ control problem is included to illustrate our results.