Synthesis of switching H<inf>2</inf> and H<inf>∞</inf> output-feedback controllers: A fuzzy supervisor approach

Abstract

In this paper the synthesis of switching multiple static output-feedback controllers for discrete-time LTI systems with state-multiplicative noise is considered which achieves a minimum bound on either the stochastic H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> or the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance levels. The proposed hybrid control scheme is based on a fuzzy supervisor which manages the combination of controllers. A convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good tracking performance in both the transient state (H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> ) and the steady state (H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> ). The stability analysis uses the Lyapunov technique, inspired from switching system theory, to prove that the system with the proposed controller remains globally stable despite the configuration changing.