Robust and reduced-order filtering: new characterizations and methods

Several challenging problems of robust filtering are addressed in this paper. First of all, for robust filtering problems, we exploit a new LMI (linear matrix inequality) characterization of minimum variance or H₂ performance, and demonstrate that it allows the use of parameter-dependent Lyapunov functions while preserving tractability of the problem. The resulting conditions are less conservative than earlier techniques, which are restricted to a fixed, that is parameter-independent, Lyapunov function. The rest of the paper is focusing on the reduced-order filter problems. New LMI-based nonconvex optimization formulations are introduced for the existence of reduced-order filters. Then, several efficient optimization algorithms of local and global optimization are proposed. Nontrivial and less conservative relaxation techniques are presented as well. The viability and efficiency of the proposed tools are confirmed through computational experiments and also comparisons with earlier methods