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In this article, an extended state observer‐based finite‐region control scheme is presented for two‐dimensional Markov jump systems with unknown mismatched disturbances. The mathematical model of the two‐dimensional Markov jump systems is built on the well‐known Roesser model. By establishing special recursive formulas and utilizing the 2‐D Lyapunov function theory, sufficient conditions are obtained, which prove that the resultant system is finite‐region bounded, if some linear matrix inequalities are achieved. Then, we provide an algorithm to solve the extended state observer‐based controller gains. With the proposed control scheme, the external disturbances can be actively rejected from the system outputs. To conclude, a numerical example based on the Darboux equation is provided to demonstrate the validity and effectiveness of the devised control scheme. [ABSTRACT FROM AUTHOR]

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]

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

This paper studies the adaptive fault estimation problems for stochastic Markovian jump systems (MJSs) with time delays. With the aid of the selected Lyapunov-Krasovskii functional, the adaptive fault estimation algorithm based on adaptive observer is proposed to enhance the rapidity and accuracy performance of fault estimation. A sufficient condition on the existence of adaptive observer is presented and proved by means of linear matrix inequalities techniques. The presented results are extended to multiple time-delayed MJSs. Simulation results illustrate that the validity of the proposed adaptive faults estimation algorithms. [ABSTRACT FROM AUTHOR]

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]

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]