Adaptive Parallel Simultaneous Stabilization of a Class of Nonlinear Descriptor Systems via Dissipative Matrix Method

Abstract

This paper investigates the adaptive parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems of a class of nonlinear descriptor systems via dissipative matrix method. Firstly, under an output feedback law, two nonlinear descriptor systems are transformed into two nonlinear differential-algebraic systems by nonsingular transformations, and a sufficient condition of impulse-free is given for two resulting closed-loop systems. Then, the two systems are combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique. Based on the dissipative system, an adaptive parallel simultaneous stabilization controller and a robust adaptive parallel simultaneous stabilization controller are designed for the two systems. Furthermore, the case of more than two nonlinear descriptor systems is investigated. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the adaptive parallel simultaneous stabilization controllers obtained in this paper work very well.