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$H_{\infty}$ feedback controls based on discrete-time state observations for singular hybrid systems with nonhomogeneous Markovian jump
Zhiyong Ye
Keywords:discrete-time state observation, stochastically stable, $H_{\infty}$feedback control, nonhomogeneous Markovian jump, singular system
      In this paper, the $H_{\infty}$-control problem for singular Markovian jump systems (SMJSs) with variable transition rates by feedback controls based on discrete-time state observations is studied. The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant. By designing a feedback controller based on discrete-time state observations, employing a stochastic Lyapunov-Krasovskii functional, and combining with the linear matrix inequalities (LMIs) technologies, sufficient conditions under the case of nonhomogeneous transition rates are developed such that the controlled system is regular, impulse free, and stochastically stable. Subsequently, the upper bound on the duration $\tau$ between two consecutive state observations and prescribed $H_{\infty}$ performance $\gamma$ are derived. Moreover, the achieved results can be easily checked by the Matlab LMI Tool Box. Finally, two numerical examples are presented to show the effectiveness of the proposed methods.