Robust stabilisation for a class of time-delay systems with triangular structure

The state-feedback control problem for a class of time-delay systems is investigated. The considered nonlinear systems have a triangular structure. By constructing a novel Lyapunov- Krasovskii functional, an adaptive state-feedback controller is designed via a backstepping method. The resulting closed-loop system is proved to be stable in the sense of uniform ultimate boundedness. Simulations are performed to verify the effectiveness of the proposed method.