Design of discrete-time multivariable PID controllers via LMI approach

Abstract

In this paper we propose a design method of discrete-time multivariable PID controllers via LMI optimizations. A discrete-time PID controller is formulated as a static output feedback controller for an augmented system and its parameters are found by a solution of LMI optimization problems. Three optimization problems are presented. One of them is based on a sufficient condition for static output feedback stabilization proposed in this paper, which is a relaxation of the condition of [7]. The others are based on H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance, respectively. The proposed method can be applied to uncertain systems with polytopic uncertainties. An illustrative example is presented.