Robust filter design with time-varying parameter uncertainty and error variance constraints

In this paper, we consider the design of robust filters for linear continuo us- and discrete-time systems subjected to time-varying parameter uncertain ties and estimation error variance constraints. The problem addressed is th e design of robust filters which do not depend on uncertainty, such that fo r all admissible time-varying parameter perturbations, the variance of the estimation error of each state is guaranteed to be not more than the indivi dual prespecified upper bound. In both continuous- and discrete-time cases, it is shown that the computation of the filter matrices calls for the solu tion of a pair of algebraic Riccati equations. Specifically, the existence conditions and the explicit expression of the desired filters are obtained. Furthermore, two illustrative examples are presented to demonstrate the ef fectiveness of the proposed design procedure.