Passivity-based stabilization of switched time-delay Hamiltonian systems with uncertainties

This paper addresses the issue of exponential stabilization for switched time-delay Hamiltonian systems with uncertainties. First, the concept of exponential passivity is proposed for nonlinear time-delay systems. For a class of time-delay Hamiltonian systems, the exponential passification conditions are given by constructing delay-dependent Lyapunov–Krasovskii functionals. Second, based on the exponential passivity of the subsystems, the criteria for the exponential stabilization of switched Hamiltonian systems are given by using the multi-storage functions and the average dwell time method. Third, the derived criteria remove the positive semi-definite constraint on damping matrices and utilize the convergence of passive subsystems to counteract the divergence of non-passive subsystems. Finally, a numerical simulation example and a circuit example are presented to verify the feasibility of the proposed method. This work only considers state delays without taking input delays or state-dependent switching laws into account, and further research will be carried out to address these issues in the future.