Robust ℋ∞-Filtering Design with Pole Placement Constraint via Linear Matrix Inequalities

Abstract

The problem of robust filtering design for continuous-time systems with convex bounded uncertainties is addressed in this paper. The aim is to determine a stable linear filter such that the filtering error system remains quadratically stable within a prespecified ℋ∞-attenuation level. Necessary and sufficient conditions for the existence of such robust filter are provided in terms of linear matrix inequalities, which can be solved efficiently through standard convex optimization procedures guaranteeing global convergence. Furthermore, as an improvement of the strategy, the filter dynamics can be constrained to some specific regions inside the left-half complex plane.