Mode-independent robust H<inf>∞</inf> control for uncertain Markovian jump systems with multiple delays in state and input

Abstract

This paper deals with the problem of delay-dependent robust stochastic stabilization and robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for uncertain markovian jump systems with multiple delays in both state and input. Based on the conditional expectation of the Markov chain's mode-set, an improved method of the delay-dependent robust stochastic stabilization for this markovian jump systems is obtained by introducing a mode-independent Liapunov-Krasovskii functional which bears no connections with any mode of the Markov chain. In terms of the input delay, we use a mode-independent state feedback to guarantee the stochastic stability of the markovian jump systems. Furthermore, in terms of a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance, a sufficient condition for the synthesis of the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for the markovian jump systems is proposed.