We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were typically oriented toward guaranteeing global bounded synchronizability, local stability of the synchronization manifold, or achieving synchronization by exerting a control action on each node. Here we start by generalizing existing results on QUAD systems to the case of PWS systems, accounting for a large variety of nonlinear coupling laws. Then, we propose that a discontinuous coupling can be used to guarantee global synchronizability of a network of N PWS agents under mild assumptions on the individual dynamics. We provide extensive numerical simulations to gain insights on larger networks.
Bibliographical noteFunding Information:
Manuscript received March 5, 2018; revised May 14, 2018; accepted May 29, 2018. Date of publication June 7, 2018; date of current version June 24, 2018. The work of S. J. Hogan was supported by COINOR and Compagnia di San Paolo. Recommended by Senior Editor M. Arcak. (Corresponding author: Marco Coraggio.) M. Coraggio and P. DeLellis are with the Department of Information Technology and Electrical Engineering, University of Naples Federico II, 80125 Naples, Italy (e-mail: firstname.lastname@example.org; email@example.com).
© 2018 IEEE.
- Switched systems
- network analysis