Adaptive parallel simultaneous stabilization of two nonlinear descriptor systems via hamiltonian function method

This paper investigates the adaptive parallel simultaneous stabilization problem of two nonlinear descriptor systems via the Hamiltonian function method. Firstly, under the Hamiltonian realizations of the two nonlinear descriptor systems and an adaptive output feedback law, two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by nonsingular transformations, and 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, the adaptive parallel simultaneous stabilization controller of two nonlinear descriptor systems is designed via the Hamiltonian function method.