Robust and reduced-order filtering: new LMI-based characterizations and methods

Several challenging problems of robust filtering are addressed in this paper. First of all, we exploit a new LMI (Linear Matrix Inequality) characterization of minimum variance or of H2 performance, and demonstrate that it allows the use of parameterdependent 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 not depending on parameters, Lyapunov functions. The rest of the paper is focusing on 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 discussed as well. The viability and efficiency of the proposed tools are confirmed through computational experiments and also through comparisons with earlier methods.