Robust filtering for uncertain linear systems with delayed states and outputs

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 H_∞ 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 H_∞ norm upper bound constraint. We establish the conditions under which the desired robust H _∞ 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