Asynchronous $l_{2}-l_{\infty}$ Filtering for Discrete-Time Singular Nonhomogeneous Markov Jump Systems

This study investigates the design of
$l_{2}-l_{\infty}$
filters for asynchronous discrete-time Singular nonhomogeneous Markov jump systems. Using a polytope set to characterize the time-varying transition probability. To describe the asynchronous phe-nomenon between system modes and filter modes, hidden Markov models are proposed. Based on the selected Lyapunov function, sufficient conditions are provided to ensure that the filtering error system is regular, causal and stochastically stable with a given
$l_{2}-l_{\infty}$
performance index. By solving the proposed conditions, an expected filter that satisfies prescribed
$l_{2}-l_{\infty}$
performance index can be constructed. In the end, the effectiveness and potential of this method were verified through two illustrative examples.