A composite feedback approach to stabilize nonholonomic systems with time varying time delays and nonlinear disturbances.

In this work, we propose a robust stabilizer for nonholonomic systems with time varying time delays and nonlinear disturbances. The proposed approach implements a composite nonlinear feedback structure in which a linear controller is designed to yield a fast response and a nonlinear feedback control law is considered to increase the system's damping ratio. This structure results in the simultaneous improvement of the steady-state accuracy and transient performance of time-delay nonholonomic systems. Asymptotic stability of the proposed feedback control approach is derived using a Lyapunov-Krasovskii functional aimed at reaching a compromise between system's transient performance and asymptotic stability. Simulation and analytical results are considered to highlight the robustness and superior performance of the proposed approach in controlling high-order-time-delay nonholonomic systems with nonlinear disturbances.