Abstract
In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched nondifferentiable systems satisfying Carathéodory conditions for the existence and uniqueness of a solution. After generalizing the classical definition of contraction to this class of dynamical systems, we give sufficient conditions for global convergence of their trajectories. The theoretical results are then applied to solve a set of representative problems such as proving global asymptotic stability of switched linear systems, giving conditions for incremental stability of piecewise smooth systems, and analyzing the convergence of networked switched systems.
Original language | English |
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Pages (from-to) | 3203-3227 |
Number of pages | 25 |
Journal | SIAM Journal on Control and Optimization |
Volume | 52 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Research Groups and Themes
- Engineering Mathematics Research Group
Keywords
- Contraction theory
- Convergence
- Networks
- Piecewise smooth systems