Simplified Design of H2-suboptimal Reduced-order Filters

Abstract

Full-order filters which are optimal with respective to the H2 norm may be formulated as convex optimization problems with Linear Matrix Inequality (LMI) constraints. Reduced-order filter design problems are non-convex, but various elegant relaxations resulting in suboptimal filters are reported in the literature. In this paper, a very simple approach is taken, where the original system is first reduced to a smaller dimension, and then a suboptimal, reduced-order filter with respect to the H2 norm is obtained through straightforward numerical optimization. The smoothing stabilization task following this problem formulation is solved by simply adding a penalty function to the cost function of the optimization problem. Finally, for large-scale filter design problems, acceleration of the H2 norm minimization utilizing another reduced-order model is used. The method shows good performance when applied on a benchmark 5-state filtering problem and on a larger 150-state filtering problem.