Robust filtering for uncertain linear systems with delayed states and outputs

This brief deals with the robust filtering problem for uncertain linear systems with delayed states and outputs. Both time-invariant and time-varying cases are considered. For the time-invariant case, an algebraic Riccati matrix inequality approach is proposed to design a robust Hinfinity filter such that the filtering process remains asymptotically stable for all admissible uncertainties, and the transfer function from the disturbance inputs to error state outputs satisfies the prespecified Hinfinity norm upper bound constraint. We establish the conditions under which the desired robust Hinfinity filters exist, and derive the explicit expression of these filters. For the time-varying case, we develop a differential Riccati inequality method to design the robust filters. A numerical example is provided to demonstrate the validity of the proposed design approach.