Almost sure state estimation for a class of nonlinear stochastic Markovian jump systems

In this paper, the almost sure asymptotic stability is investigated for the state estimation problem of a general class of nonlinear stochastic Markovian jump systems. A nonlinear state estimator with Markovian switching is first proposed, and then a sufficient condition is given which guarantees the almost sure asymptotic stability of the dynamics of the estimation error. Based on this condition, some simplified criteria are deduced by taking special forms of the Lyapunov functions. Subsequently, an easy-to-verify procedure is put forward for the state estimation problem of the linear stochastic Markovian jump system. Finally, two numerical examples are used to illustrate the effectiveness of the main results.