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This paper studies the robust stochastic stability problem for a class of Markov jump systems with norm bounded uncertain parameters and distributed time-delays. Integral inequality techniques together with Lyapunov-Krasovskii functional approach are employed to develop new delay-dependent sufficient conditions for stochastic stability. The main results are derived via linear matrix inequalities formulation. Simulation examples illustrate the effectiveness of the developed techniques. [ABSTRACT FROM AUTHOR]

Abstract: The peak-to-peak filtering problem is studied for a class of Markov jump systems with uncertain parameters. By re-constructing the system, the dynamic filtering error system is obtained. The objective is to design a peak-to-peak filter such that the induced gain from the unknown inputs to the estimated errors is minimized or guaranteed to be less or equal to a prescribed value. By using appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions are initially established on the existence of mode-dependent peak-to-peak filter which also guarantees the stochastic stability of the filtering error dynamic systems. The design criterions are presented in the form of linear matrix inequalities and then described as an optimization problem. Simulation results demonstrate the validity of the proposed approaches. [Copyright &y& Elsevier]

Abstract: The unbiased H ∞ filtering problem is studied for stochastic Markov jump system with constant and neutral time-delays. By re-constructing the system, the dynamic filtering error characteristics of unknown inputs and time-delays are obtained. A sufficient condition is initially established on the existence of mode-dependent unbiased H ∞ filter of constant time-delay system using stochastic Lyapunov–Krasovskii function. Then, the unbiased H ∞ filter is also designed for the jump system with constant and neutral time-delays. The design criterions are presented in the form of linear matrix inequality. Finally, the unbiased H ∞ filtering problems are described as optimization algorithms. Numerical examples illustrate the effectiveness of the developed techniques. [Copyright &y& Elsevier]