Finite‐time adaptive stabilization and H∞$$ {H}_{\infty } $$ control for a class of nonlinear Hamiltonian singular systems with parametric perturbations

Abstract This article addresses the finite‐time adaptive stabilization and finite‐time adaptive control problems of a class of nonlinear Hamiltonian singular systems with parametric perturbations. Under the suitable state feedback control scheme, a dissipative differential‐algebraic form of the nonlinear Hamiltonian singular system is obtained. According to this dissipative form, the finite‐time adaptive stabilization of the nonlinear Hamiltonian singular system with unknown parametric perturbations is investigated using the Hamiltonian function method. Then, considering the system with the external disturbances, a finite‐time adaptive controller is designed. Finally, the simulation results of the nonlinear singular circuit system demonstrate the efficacy of the controller designed in this article.