Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method. Issue 12 (August 2019)

• Record Type: Journal Article
• Authors: Yang, Renming; Sun, Liying; Zhang, Guangyuan; Zhang, Qiang
• Is Part Of: Journal of the Franklin Institute. Volume 356:Issue 12(2019)
• Page Start: 5961
• Page End: 5992
• Publication Date: 2019-08
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2019.04.033
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This paper investigates the finite-time stability (FTS) and finite-time stabilization for a class of nonlinear singular time-delay Hamiltonian systems, and proposes a number of new results on these issues. Firstly, an equivalent form is obtained for the nonlinear singular time-delay Hamiltonian systems by the singular matrix decomposition method, based on which some delay-independent and delay-dependent conditions on the FTS are derived for the systems by constructing a kind of novel Lyapunov function. Secondly, we use the equivalent form as well as the energy shaping plus damping injection technique to investigate the finite-time stabilization problem for a class of nonlinear singular port-controlled Hamiltonian (PCH) systems with time delay, and present a specific control design procedure for the systems. Finally, we give several illustrative examples to show the effectiveness of the results obtained in this paper.