Robust Gain-scheduled H∞ Estimation of State-multiplicative Systems

The theory of robust gain scheduling estimation of polytopic-type uncertain continuous-time state-multiplicative stochastic systems is investigated. We apply a vertex-dependant approach for the solution of the $H_{\infty }$ estimation of these systems which considerably reduces the overdesign associated with the classical design of the robust filter. Whereas the usual solution applies a single Lyapunov function for the whole parameter range of the uncertain system, in this study we apply the Finsler lemma one additional time. The later strategy greatly improves the performance of the robust gain scheduled filter where on-line measurement is used to improve the estimation. The advantage of the latter design is demonstrated via a numerical example that applies several design methods for the solution of the robust estimation problem.