Simultaneous H₂/H∞ control of uncertain jump systems with functional time-delays

Abstract

<jats:title>Abstract</jats:title><jats:p>This paper presents new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state in which the time‐delays are mode dependent. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process and the uncertainties are norm‐bounded. We construct an appropriate Lyapunov–Krasovskii functional and design a simultaneous ℋ︁<jats:sub>2</jats:sub>/ℋ︁<jats:sub>∞</jats:sub> controller which minimizes a quadratic ℋ︁<jats:sub>2</jats:sub> performance measure while satisfying a prescribed ℋ︁<jats:sub>∞</jats:sub>‐norm bound on the closed‐loop system. It is established that sufficient conditions for the existence of the simultaneous ℋ︁<jats:sub>2</jats:sub>/ℋ︁<jats:sub>∞</jats:sub> controller and the associated performance upper bound are cast in the form of linear matrix inequalities. Simulation results are provided and extension to the case where the jumping rates are subject to uncertainties is presented. Copyright © 2007 John Wiley &amp; Sons, Ltd.</jats:p>