Nonlinear damping control for interconnected nonlinear systems

In this paper, we propose enhanced nonlinear damping control for a class of singularly perturbed interconnected nonlinear systems (SPINSs). The proposed method transforms SPINS into a feedback connection of two subsystems. Then, nonlinear damping is implemented to improve the transient behavior of slow subsystem. The proposed method provides weighting factors for each tracking error, which enable the design of the energy function to shape the tracking performance for each state. We also design an augmented state observer to estimate unknown disturbances and unmeasurable states. Using a composite Lyapunov function, we prove that the origin of the tracking error dynamics is globally exponentially stable. It is also analyzed that the tracking errors are also globally uniformly ultimately bounded for a time-varying bounded disturbance. Simulations were performed to evaluate the tracking performance of the proposed method. Simulation results validate the effectiveness of the proposed method.