Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method

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. (C) 2019 Published by Elsevier Ltd on behalf of The Franklin Institute.