New approaches on adaptive stabilization for uncertain systems subject to multiple time delays

This paper explores the stabilization issue of uncertain systems subject to multiple time delays under adaptive robust control. Without imposing matching constraints on uncertain system parameter matrices, an adaptive robust controller is utilized to ensure the asymptotic stability of the closed-loop system. A delay-independent approach is proposed for determining the gain and update law using Lyapunov functionals and thoroughly considering the input matrix. Then, a delay-dependent approach is presented by utilizing more complicated Lyapunov functionals and introducing some slack matrix variables. Numerical examples illustrate that the methods proposed herein exhibit decreased conservatism and improved applicability compared to existing methods.