Adaptive observer design for a class of descriptor nonlinear systems

Abstract This paper deals with the design of adaptive observer for a class of bilinear time delay systems. First, this problem is investigated in the full order case and it is then extended to the reduced order one. 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 (LMIs) on the vertices of a convex polytope. A relevant example is provided to show the feasibility and the high performances of our results.