Synthesis for Jumping Time-Delay Systems using Transformation Methods

A new transformation method is developed for the H∞ analysis and synthesis of a class of uncertain time-delay systems with Markovian jump parameters. In these systems, 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. The time-delay factor is constant. Complete results for delay dependent stochastic stability and stabilization criteria are developed for all admissible uncertainties. Then a dynamic output feedback controller is designed such that the closed-loop stochastic stability and a prescribed H∞-performance are guaranteed. All the developed results are cast in the format of linear matrix inequalities