Global asymptotic stabilisation and H∞ control for a class of nonlinear Hamiltonian singular systems with delays and saturation

This paper studies the global asymptotical stabilisation and $H_\infty $H∞ control problems for a class of nonlinear Hamiltonian singular systems (NHSSs) with time-varying delays as well as input saturation. The delays existing in input and output are assumed to be bounded. A global asymptotic stabilisation controller is first proposed by output feedback, and $H_\infty $H∞ control performance is achieved for the discussed system when external disturbances are considered. Based on the structural characteristic of the NHSSs, the closed-loop system under the output feedback controller is transformed equivalently into slow subsystem and fast subsystem. Different criterions are identified to guarantee that the resulting closed-loop system is asymptotically stable and the γ-dissipative inequalities holds in the presence of disturbances, respectively. Finally, the validity of our proposed results is illustrated by a numerical example.