Delay-dependent robust H∞ control for uncertain stochastic time-delay systems

Abstract

<jats:title>Abstract</jats:title><jats:p>This paper investigates the robust <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> control problem for stochastic systems with a delay in the state. Sufficient delay‐dependent conditions for the existence of state‐feedback controllers are proposed to guarantee mean‐square asymptotic stability as well as the prescribed <jats:italic>H</jats:italic><jats:sub>∞</jats:sub> performance for the closed‐loop systems. Moreover, the results are further extended to the stochastic time‐delay systems with parameter uncertainties, which are assumed to be time‐varying norm‐bounded appearing in both the state and the input matrices. The appealing idea is to partition the delay, which differs greatly from the most existing results and reduces conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed techniques. Copyright © 2009 John Wiley &amp; Sons, Ltd.</jats:p>