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

• Published in: Asian journal of control Vol. 26; no. 3; pp. 1309 - 1322
• Main Authors: Chen, Yufei, Liu, Qihuai, Zhou, Xia
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 01.05.2024
• Subjects: Control systems; Feedback control; finite‐time stability; H-infinity control; Hamiltonian functions; input saturation; Nonlinear control; Nonlinear systems; time‐varying delay
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.3253

In this paper, we investigate the finite‐time stability (FTS) and H∞$$ {H}_{\infty } $$ 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 H∞$$ {H}_{\infty } $$ feedback control is designed for the nonlinear Hamiltonian systems. Finally, the validity of the proposed results is demonstrated by a numerical example.