Worst case control of uncertain jumping systems with multi-state and input delay information

In this paper, the problem of worst case (also called H∞H∞) Control for a class of uncertain systems with Markovian jump parameters and multiple delays in the state and input is investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state, input and delayed-state matrices. The time-delay factors are unknowns and time-varying with known bounds. Complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak-delay dependent stochastic stability with a prescribed H∞H∞-performance. The solutions are provided in terms of a finite set of coupled linear matrix inequalities (LMIs). Application of the developed theory to a typical example has been presented.