Robust H_∞ filtering for Delta operator formulated systems with circular pole and error variance constraints

The problem of robust H_∞filtering for the Delta operator formulated uncertain discrete time systems with error variance and circular pole constraints is studied. The system under consideration is subject to norm-bound time-invariant uncertainties in both the state and output matrices. A robust filter is designed to guarantee that the filtering process is D-stable, the steady-state estimation error variance of each state is not more than the individual prespecified value, and the H_∞norm of the transfer function from noise inputs to error state outputs meets given upper bound. In terms of algebraic matrix inequality approach, such multi-objective H_∞filtering problem is solved, and both the existence conditions and explicit expression of the desired filter are developed. The proposed results bring previous related conclusions of continuous and discrete-time systems into the unified Delta form.