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

This paper addresses several challenging problems of robust filtering. We derive new linear matrix inequality (LMI) characterizations of minimum variance or H₂ performance and demonstrate that they allow 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 fixed (not parameter-dependent) Lyapunov functions. The remainder of the paper discusses reduced-order filter problems. New LMI-based nonconvex optimization formulations are introduced for the existence of reduced-order filters, and 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 approaches are then illustrated through computational experiments and comparisons with existing methods