Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties

The dynamic output feedback control problem is considered for a class of systems with multiple time delays and nonlinear uncertainties. Based on the control input matrix and output matrix, we decompose the system into two subsystems. The dynamic compensator is designed for the first subsystem, and then the output feedback controller is constructed based on the compensator and the second subsystem. By using the introduced new Lyapunov–Krasovskii functional, we show that the solution of the resultant closed-loop system converges exponentially to an adjustable bounded region. Compared with the previous works, the developed controller in this paper is memoryless and smooth, which only uses the system output. The control design conditions are relaxed because of the developed dynamic compensator. The result is further extended to the general nonlinear case. The corresponding dynamic nonlinear output feedback control method is proposed. Finally, simulations are performed to show the potential of the proposed methods.