A new design of robust H2H2 filters for uncertain systems

In this paper, a structured polynomial parameter-dependent approach is proposed for robust H2H2 filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with ss vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust H2H2 filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of ss matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples.