Filtering of Switching Systems via a Minimax Approach

This paper considers the problem of state estimation for discrete-time systems whose dynamics switches within a finite set of linear stochastic behaviors. The solution of the filtering problem depends on the a priori informations available on the switching process. In most papers the switching process is modeled by a finite-state Markov chain, with a known transition matrix. In this case the computation of the optimal filter is cumbersome and most papers deal with approximate filters. This paper considers systems in which the switching process is not statistically characterized. Such systems can be regarded as uncertain regular systems arid can be transformed into singular systems with uncertainties only on the second order noise statistics. This allows to develop minimax linear filters, i.e. filters that give, the minimum error variance in the worst case of noise statistics.