Functional adaptive H∞ observer design for a class of bilinear systems with time delays

Abstract This chapter deals with the design of an H ∞ adaptive observer with a reduced order for a class of bilinear time-delay systems. The proposed observers allow the joint estimation of the state and the unknown parameter vectors. A Lyapunov-Krasovskii approach is used to deduce the stability conditions, given in terms of the solvability of linear matrix inequalities on the vertices of a convex polytope. A relevant example is provided to show the feasibility and the high performances of our results.