Finite-Time Control Case

Finite-time boundedness (FTB) describes the boundedness of system states. It required that system states cannot exceed a given threshold during a finite time interval. The existing results on Markov jump singularly perturbed systems (MJSPSs) mainly focused on the stochastic stability in infinite-time interval. This chapter investigates the problem of finite-time asynchronous passive control for MJSPSs, in which the partly known probability information exists in the transition probability matrix and the observation probability matrix simultaneously. To solve the asynchronous phenomenon between the system mode and controller mode, a hidden Markov model with general probabilities is introduced. By using the Lyapunov function approach, a set of sufficient conditions are obtained to guarantee the MJSPSs are finite time boundedness and passive performance. Then, the asynchronous controller gain is obtained by solving the linear matrix inequalities independent of singularly perturbed parameters (SPSs). Finally, an examples is given to verify the effectiveness of the proposed control law.