Robust vertex‐dependent H_∞ and H₂ estimation for stochastic linear systems

Abstract

Summary We consider linear continuous‐time systems with multiplicative noise and polytopic‐type parameter uncertainty, and we address the problems of H∞ and H2 filtering of these systems. These problems are solved by applying a vertex‐dependent Lyapunov function that considerably reduces the overdesign associated with the classical design that is based on a single Lyapunov function for the whole parameter range. A new approach of the Finsler lemma is used that decreases the overdesign entailed in the usual derivation of the robust estimation problem. The developed theory is also extended to the robust gain scheduling case where online measurement is used to improve the estimation. Two examples are given that demonstrate the tractability and applicability of the design methods.

Vertex‐dependent filtering of retarded uncertain state‐multiplicative noisy systems

“…The application of the Finsler lemma to the stochastic filtering problem has already been applied in the past to the delay free case 30 . In fact, in Reference 30, this lemma has been applied twice and was found to reduce the conservatism associated with the quadratic solution.…”

“…The application of the Finsler lemma to the stochastic filtering problem has already been applied in the past to the delay free case 30 . In fact, in Reference 30, this lemma has been applied twice and was found to reduce the conservatism associated with the quadratic solution. Unfortunately, the method that was adopted in Reference 30 does not apply here because of the considerable differences between the BRL for stochastic delay‐free systems and the BRL that is obtained for delayed system.…”

“…In fact, in Reference 30, this lemma has been applied twice and was found to reduce the conservatism associated with the quadratic solution. Unfortunately, the method that was adopted in Reference 30 does not apply here because of the considerable differences between the BRL for stochastic delay‐free systems and the BRL that is obtained for delayed system. Since the filtering solution is based on the BRL, another way of coping with the uncertainty should be adopted.…”