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The paper deals with the problem of non-fragile observer-based passive control for a class of Markovian jumping systems (MJSs) subjected to uncertainties, nonlinearities and time-delays. Based on the Takagi–Sugeno fuzzy models, the dynamics of mode-dependent non-fragile state observer and feedback controller system and the combined closed-loop fuzzy dynamic MJSs are constructed. A sufficient condition for passivity and stochastic stability of the combined system is derived and proved by means of the Lyapunov–Krasovskii functional methods and linear matrix inequalities (LMIs) techniques. The non-fragile passive controller and observer parameters can be solved directly by using the existing LMIs optimization techniques. Finally, a numerical simulation is given to illustrate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: The unbiased H ∞ filtering problem is considered for a class of Markov jump systems (MJSs) with distributed time-delays. Based on the selected Lyapunov–Krasovskii functional, it gives a sufficient condition for the existence of the mode-dependent unbiased H ∞ filter such that the filtering error dynamic MJSs is stochastically stable and satisfies a prescribed level of H ∞ disturbance attenuation in an infinite time-interval. The design criterions are presented in the form of linear matrix inequality techniques, and then are described as the optimization problems. At last, two numerical examples are employed to illustrate the effectiveness of the developed techniques. [Copyright &y& Elsevier]

Abstract: This paper studies the robust fault detection filter (RFDF) design problems for uncertain nonlinear Markov jump systems with state delays and parameter uncertainties. By means of Takagi–Sugeno fuzzy models, the dynamics of filtering error generator and the fuzzy RFDF system are constructed. With the aid of the selected weighting matrix function, the design objective is to find an optimal RFDF which results in a minimal difference between the reference model (ideal solution) and the RFDF (real solution) to be designed. A sufficient condition is firstly established on the stochastic stability by using stochastic Lyapunov–Krasovskii functional approach. Then in terms of linear matrix inequalities techniques, sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as an optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences. [Copyright &y& Elsevier]

Abstract: The stochastic finite-time boundedness problem is considered for a class of uncertain Markovian jumping neural networks (MJNNs) that possess partially known transition jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By selecting the appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions of stochastic finite time boundedness of MJNNs are presented and proved. The boundedness criteria are formulated in the form of linear matrix inequalities and the designed algorithms are described as optimization ones. Simulation results illustrate the effectiveness of the developed approaches. [Copyright &y& Elsevier]

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]