Gain-Scheduled H∞-Control for Discrete-Time Polytopic LPV Systems Using Homogeneous Polynomially Parameter-Dependent Lyapunov Functions

This paper presents H∞ performance analysis and control synthesis for discrete-time linear systems with time-varying parameters. The parameters are assumed to vary inside a polytope and have known bounds on their rate of variation. The geometric properties of the polytopic domain are exploited to derive parameter-dependent linear matrix inequality conditions that consider the bounds on the rate of variation of the parameters. A systematic procedure is proposed to construct a family of finite-dimensional relaxations based on Pólya's Theorem and a homogeneous polynomially parameter-dependent parameterization of arbitrary degree for the Lyapunov matrix. A numerical example illustrates the proposed approach.