State transformation for H∞ control of uncertain jumping delayed systems

A new state transformation exhibiting the delay-dependent behaviour for a class of uncertain delayed systems with Markovian jump parameters is developed to solve the problem of H∞ control. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the parametric uncertainties are assumed to be real, timevarying and norm-bounded that appear in the state, input and delayed-state matrices. The input and state delays are known. Complete results for instantaneous state feedback control designs are established which guarantee the strong-delay dependent stochastic stability with a prescribed H∞-performance. The solutions are provided in terms of a finite set of coupled linear matrix inequalities. A numerical example is given to show the potential of the proposed techniques