A descriptor approach to simulataneous H2/H control of jumping time-delay systems

Abstract

In this paper, we develop a descriptor approach to simultaneous H₂/H_∞ control design for a class of uncertain time‐delay systems with Markovian jump parameters. The rationale behind this approach is to exhibit the delay‐dependence dynamics in the design procedure. In the system under consideration, the delay factor is constant, the jumping parameters are modelled as a continuous‐time, discrete‐state Markov process and the uncertainties are assumed to be real, time‐varying and norm‐bounded. A state‐feedback control is derived for both the nominal and uncertain systems such that the H₂‐performance measure is minimized while guaranteeing a prescribed H_∞‐norm bound on the controlled system. All the developed results are cast in the format of linear matrix inequalities (LMIs) and numerical examples are presented.