Kalman Filtering for Discrete-Time Switched System with Uncertainties

In this paper, a Kalman filter problem of discrete switched systems is discussed and considered, in which the system has norm-bounded and time-varying structure uncertainties, both for the state and measurement (sensor) equations/functions. In this paper, first, the stochastic stabilization condition of the system is investigated, and then a linear state filter, or known as estimator/observer, is constructed to make the covariance matrices of the estimation errors bounded, for all the structure uncertainties. The results show that the filter can be expressed by the solutions of two Riccati difference inequations, and the solutions of these two difference functions are proper for on-line recursive calculation. Finally, an example is set to show the results of the proposed method in this paper.