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

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.