Kybernetika 37 no. 4, 381-396, 2001

Nonlinear bounded control for time-delay systems

Germain Garcia and Sophie Tarbouriech


A method to derive a nonlinear bounded state feedback controller for a linear continuous-time system with time-delay in the state is proposed. The controllers are based on an $e$-parameterized family of algebraic Riccati equations or on an $e$-parameterized family of LMI optimization problems. Hence, nested ellipsoidal neighborhoods of the origin are determined. Thus, from the Lyapunov-Krasovskii theorem, the uniform asymptotic stability of the closed-loop system is guaranteed and a certain performance level is attained through a quadratic cost function.