H2 Control for Discrete-time System with Multiplicative Controller Gain Variations

Abstract

This paper is concerned with the problem of a non- fragile H ₂ controller design for linear discrete-time systems in the presence of controller gain variations. The controller gain to be designed is assumed to have multiplicative gain variations. The purpose of this work is to design a dynamic output feedback controller such that, for all admissible multiplicative controller gain variations, the closed-loop systems are asymptotically stable and have an H ₂ performance criterion via matrix inequalities. The sequentially linear programming method (SLPMM) is applied to solve the matrix inequalities. Numerical example is given to illustrate the design procedure and its effectiveness.