Finite-time H∞ control for a class of nonlinear descriptor Hamiltonian system

This paper uses the good structure characteristics of Hamilton system to study the finite-time stability problem of nonlinear descriptor Hamiltonian system with the constant structure matrices. Firstly, the system is transformed into Hamiltonian differential-algebra system by the equivalent transformation of the system. Then, the system is changed into a strict dissipative Hamiltonian form through state feedback. Based on this dissipative form, this paper not only studies the finite-time stabilization of the nonlinear descriptor Hamiltonian system but also designs an H controller of the nonlinear descriptor Hamiltonian system with an external disturbances by applying the existing stabilization results and the detectable conditions of the generalized zero-energy-gradient of the system.