Extended Robust H_2 and H_∞ Filter Design for Discrete Time-Invariant Linear Systems with Polytopic Uncertainty

摘要

This paper is concerned with the problem of robust H_2 and H_∞ filter design for discrete-time linear time-invariant systems with polytopic parameter uncertainties. Less conservative robust H_2 and H_∞ filter design procedures are proposed in terms of single-parameter minimization problems with linear matrix inequality constraints. To this end, we generalize the filter structures available in the literature to date in such a way that the filter's next state is built by summing the filter's states over several samples from the past to the present. For stability of the filtering error system, the homogeneous polynomial parameter-dependent Lyapunov functions are employed. Finally, illustrative examples are given to demonstrate the merits of the proposed methods.