Robust H∞ filter design for the delta operator formulated systems with parameter uncertainty

This paper is concerned with the problem of robust H_∞ filtering for the delta operator formulated discrete-time systems with norm-bound parameter uncertainties in both the state and output matrices. The purpose of this problem addressed is to design a linear filter such that the filtering process is asymptotically stable and the transfer function from the exogenous noise inputs to the error state outputs meets a given H_∞ norm upper bound constraint for all admissible uncertainties. A sufficient condition for the existence of such a filter is obtained in terms of algebraic matrix inequality approach, and the explicit expression of the desired filter is also derived. The main results are then extended to robust H_∞ filter design for delta operator formulated state-delayed systems.