On the Design of Functional Observers for Multi-Delayed Linear Systems

This paper considers the problem of designing functional observers for multi-delayed linear systems. It produces a general presentation and practical method for the design of the observers examined by Darouach in [14]. Based on the Lyapunov-Krasovskii functional theory, the stability conditions are obtained in terms of linear matrix inequalities (LMIs). Sufficient conditions for the stability of the observers with delays are proposed. Constant and variable delays are taken into account. Numerical examples are awarded to show how the results presented in [14] cannot be applied to the system proposed in this paper.