Robust $H_{\infty}$ dynamic output feedback control of discrete LPV repetitive processes

Abstract

This paper is concerned with the problem of robust $\mathrm{H}_{\infty}$ dynamic output feedback controller design for discrete linear parameter-varying (LPV) repetitive processes which are a distinct class of non-linear two-dimensional systems of both system theoretic and application interests. The attention is focused on the design of full-order $\mathrm{H}_{\infty}$ dynamic output feedback controller, which guarantees the closed-loop system to be asymptotically stable and the disturbance attenuation levels in $\mathrm{H}_{\infty}$ senses. The numerical is more advantageous implemented by the introduction of a slack matrix, which exhibits a kind of decoupling between the parameter-dependent Lyapunov functions (PDLF) and the system matrices. A sufficient condition is derived for existence of robust $\mathrm{H}_{\infty}$ dynamic output feedback controllers in terms of the parameterized linear matrix inequalities (PLMIs) technology, which is corresponding to the infinite dimensional convex optimization problem. Therefore, the corresponding controller design is cast into a convex optimization problem of the finite parameter linear matrix inequalities by using approximate basis function and the gridding technique. A numerical example is included to illustrate the effectiveness of the proposed design method.