Robust H_∞ filtering for Delta operator formulated uncertain systems with error variance constraints

The problem of robust H ∞ filtering for the Delta operator formulated uncertain discrete time systems with error variance constraints is considered. The purpose is to design a linear filter such that for the system with norm bound parameter uncertainties in both the state and output matrices, the following three performance requirements are simultaneously satisfied:1) The filtering process is asymptotically stable; 2) The steady state variance of the estimation error of each state is not more than the individual prespecified value; 3) The transfer function from the exogenous noise inputs to the error state outputs meets a given H ∞ norm upper bound constraint. Sufficient conditions for the filter to meet H ∞ performance and steady state estimation error variance constraints are obtained in terms of algebraic matrix inequality approach, and the explicit expression of the desired filter is also derived. The proposed results can also bring existing H ∞ filtering conclusions of continuous time and discrete time systems into the unified Delta framework.