Retarded state-multiplicative stochastic systems - Robust H _∞ and H ₂ vertex-dependent filtering

We consider linear continuous-time retarded systems with multiplicative noise and polytopic type parameter uncertainty and we address the problems of (Formula presented.) and (Formula presented.) general filtering of these systems. These problems are solved by applying a modified version of the descriptor method that leads to a considerable reduction in the over-design associated with the ”quadratic” solution that assigns a single Lyapunov function to all the points in the uncertainty polytope. The theory is extended to the robust gain-scheduling case where on-line parameter measurement is exercised in the estimation process. Two examples are given that demonstrate the superiority of our solution method. The first example relates to a simple second order system whereas the second example is one of altitude estimation taken from the field of aerospace engineering.