Memoryless adaptive controller design for uncertain polynomial systems with multiple time delays

The stabilization problem is investigated for a class of uncertain systems with multiple time-varying delays. The considered system includes the uncertain nonlinear time delay functions, whose bounds are in the form of polynomial-type functions with unknown coefficients. The system is decomposed into two subsystems based on the input matrix. For the first subsystem, a time delay dependent linear virtual control input is constructed. Then, a memoryless state feedback controller is designed based on backstepping method. By employing new Lyapunov-Krasovskii functional, we show that the closed-loop system is exponentially stable. Finally, simulations are conducted to verify the effectiveness of the proposed method.