Stabilization of uncertain systems with multiple time-delays via adaptive robust control

This paper deals with the adaptive robust control problem for uncertain systems with multiple time-delays. It is assumed that the uncertainties are norm-bounded, but their bounds are not necessarily known. While in most existing literature, in addition to this assumption, it is necessary to satisfy a matching condition. This condition is restrictive and is not met in many practical systems. This requirement is removed in this study. Hence, the control scheme is applicable for a wider range of systems. Based on an appropriate Lyapunov–Krasovskii functional, the sufficient condition for the existence of an adaptive robust controller is obtained in terms of linear matrix inequalities. The designed controller ensures asymptotic stability of the closed-loop system. Finally, the simulation results illustrate the validity of the proposed control methodology.