Gain-Scheduled H∞ Control for Discrete-Time Polynomial LPV Systems Using Homogeneous Polynomial Path-Dependent Lyapunov Functions

Abstract This paper provides linear matrix inequality (LMI) analysis and synthesis conditions for the design of H ∞ robust and gain-scheduled static output feedback controllers, for discrete-time linear parameter-varying systems. It is assumed that the system matrices have a homogeneous polynomial dependence of arbitrary degree on the time-varying scheduling parameters, which are assumed to vary inside a polytope and to have known bounds on their rates of variation. The geometric properties of the polytopic domain are exploited in order to derive a finite set of LMIs that takes into account bounds on the variation rate of the scheduling parameters. LMI conditions are obtained using a quadratic Lyapunov function with a homogeneous polynomial dependence on the scheduling parameters at successive instants of time. Numerical results show the benefits of the proposed approach.