FILTERING OF SWITCHING SYSTEMS VIA A SINGULAR MINIMAX APPROACH

This paper considers the problem of state estimation for discrete-time systems whose dynamics switches within a ¯nite set of linear stochastic behaviors. In recent years such systems are receiving a growing attention because of their importance from an applicative point of view, in that switching phenomena are normally present in many engineering problems. The solution of the ¯ltering problem depends on the amount of the a priori information about the switching process. In most papers the switching process is modeled by a discrete Markov chain, with a known transition matrix. For this problem the exact computation of the optimal ¯lter is cumbersome, and most papers deal with the problem of computing approximate ¯lters. In this paper a switching process, that is not statistically characterized, is considered. The system is regarded as an uncertain regular system and it is transformed into a singular system with uncertainties only on the second order statistics of noises. This allows us to develop a minimax linear ¯lter, that is the ¯lter that gives the minimum error variance in the worst case of noise statistics