A parameter-dependent Lyapunov function based approach to H_∞-control of LPV discrete-time systems with delays

In this paper we study the problem of H_∞ control of linear parameter-varying (LPV) discrete-time systems with delays. In an LPV system, the state-space matrices are a function of time-varying parameters which are assumed to be real-time measurable. We utilize a parameter-dependent Lyapunov function to establish a delay-dependent H_∞ performance condition for the LPV system with unknown but bounded delays. On the basis of the H_∞ performance condition established, we develop a linear matrix inequality (LMI) based H_∞ control strategy. We show that solving the related LMI optimization problem paves the way for designing a H_∞ controller for the LPV discrete-time system with delays. We also use a numerical example to demonstrate the application of the presented H_∞ controller design method.