New results on finite‐time stability and H_∞control for nonlinear Hamiltonian systems

Abstract

In this paper, we investigate the finite‐time stability (FTS) and control of nonlinear Hamiltonian systems with time‐varying state delays and output delays subject to input saturation. By introducing a new class of Lyapunov–Krasovskii (L‐K) functionals and the assumption about the Hamiltonian function, we present a delay‐dependent FTS criterion. Then, a finite‐time feedback control is designed for the nonlinear Hamiltonian systems. Finally, the validity of the proposed results is demonstrated by a numerical example.

Stability of port-Hamiltonian systems with mixed time delays subject to input saturation

“…In recent years, many papers consider the stability of nonlinear systems with time delays and input saturation constraints in the framework of PH systems [5,28,33,35]. Cao et al proposed delay-dependent and delay-independent stability conditions for linear time-delay systems with input saturation by using the Lyapunov-Krasovskii functional method in [3].…”