Asynchronous Finite-Time Filtering of Markov Jump Nonlinear Systems and Its Applications

In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate. The so-called asynchronization means that the filter's modes do not synchronize with the system's modes. Both the stochastic finite-time boundedness (FTBs) problem and the stochastic input-output finite-time stability (IO-FTSy) problem are involved. By resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques, some interesting results are derived to verify the properties of the stochastic FTBs and the stochastic IO-FTSy of the asynchronous filtering error system. The asynchronous filter parameters can be reduced to the solvability of some convex optimization problems. Finally, a single-link robot arm and a tunnel diode circuit are applied to elucidate the proposed algorithms.