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This paper focuses on the issue of the finite-region H ∞ asynchronous control scheme, which is devoted to the transient behavior of a class of two-dimensional Markov jump systems. The disquisitive system is characterized based upon a Roesser model. Considering the fact that there exists an asynchronous phenomenon between the controlled plant and the controller, we introduce a hidden Markov model to address the non-synchronization. By resorting to a given conditional probability matrix, the mode jumps between the controlled plant and the controller are determined. To conclude, an example is employed to illustrate the potential applications of the devised approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stochastically finite-time L 2 control problem for a class of positive stochastic Poisson jump systems (PSPJSs). By introducing a novel mode decoupling technique, some necessary and sufficient conditions are given to guarantee the stochastic finite-time boundedness of the input-free PSPJSs. Then, a proper mode-dependent finite-time state feedback controller is designed such that the positiveness, stochastic finite-time boundedness and the specified L 2 disturbance attenuation performance are attained simultaneously for the closed-loop SPJSs. Finally, two examples are given to show the feasibility and validity of the proposed methods. [ABSTRACT FROM AUTHOR]