Enhanced nonlinear damping for a class of singularly perturbed interconnected nonlinear systems

Abstract

In this paper, we propose a method of enhanced nonlinear damping control for a class of singularly perturbed interconnected nonlinear systems (SPINSs). Instead of simply canceling out the interconnection between slow and fast subsystems, the proposed method transforms SPINS into a feedback connection of two output strictly passive subsystems. Then, enhanced 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 energy function to be designed 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 globally uniformly ultimately bounded for a time-varying bounded disturbance. Experiments were performed to evaluate the tracking performance of the proposed method and our results validate the effectiveness of the proposed method.