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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: This paper provides the observer-based finite-time control problem of time-delayed Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The observer-based finite-time H ∞ controller via state feedback is proposed to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible disturbances and unknown time-delays. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic robust control performance of time-delay jump systems are derived. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The presented results are extended to time-varying delayed MJSs. Simulation results illustrate the effectiveness of the developed approaches. [Copyright &y& Elsevier]

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]

• An ETS is proposed to reduce energy consumption. • An event-triggered-based controller is designed for MJCPSs. • The uniform upper/lower bounds are used to describe DoS attacks. • Sufficient conditions are given to stabilize the MJCPSs. This paper is concerned with the event-triggered-based H ∞ control problem for Markov jump cyber-physical systems against denial-of-service attacks. The uniform upper and lower bounds are used to describe the characteristics of aperiodic denial-of-service attacks. An event-triggered scheme is introduced to reduce the waste of resources and avoid communication channel congestion. Based on multi-Lyapunov functions, sufficient conditions are proposed to guarantee the asymptotic mean-square stability and H ∞ performance of the switched closed-loop Markov jump cyber-physical systems. By solving linear matrix inequalities, the event-triggered-based controller gain matrices, and H ∞ performance index are obtained. In the simulation, an F-404 aircraft engine system is employed to clarify the validity of the proposed event-triggered-based controller design approach in face of denial-of-service attacks. [ABSTRACT FROM AUTHOR]