Stability analysis of switched homogeneous time-delay systems under synchronous and asynchronous commutation

Alexander Aleksandrov (1) , Denis Efimov (2, 3)

1 SPBU - Saint Petersburg State University
2 VALSE - Finite-time control and estimation for distributed systems
3 ITMO - National Research University of Information Technologies, Mechanics and Optics [St. Petersburg]

In this work, stability analysis for a class of switched nonlinear time-delay systems is performed by applying Lyapunov-Krasovskii and Lyapunov-Razumikhin approaches. It is assumed that each subsystem in the family is homogeneous (of positive or negative degree) and asymptotically stable in the delay-free setting. The cases of existence of a common or multiple Lyapunov-Krasovskii functionals and a common Lyapunov-Razumikhin function are explored. The scenarios with synchronous and asynchronous switching are considered, and it is demonstrated that depending on the kind of commutation, one of the frameworks for stability analysis outperforms another, but finally leading to similar restrictions for both types of switching (despite the asynchronous one seems to be more demanded). The obtained results are applied to mechanical systems having restoring forces with real-valued powers.

Mots clés: Switched systems; Time-delay systems; Homogeneous systems; Lyapunov-Krasovskii approach; Lyapunov-Razumikhin approach

Domaines: Automatique / Robotique

Alexander Aleksandrov, Denis Efimov. Stability analysis of switched homogeneous time-delay systems under synchronous and asynchronous commutation. Nonlinear Analysis: Hybrid Systems, 2021, 42, ⟨10.1016/j.nahs.2021.101090⟩. ⟨hal-03314543⟩