Continuity Conditions for Piecewise Quadratic Functions on Simplicial Conic Partitions Are Equivalent
Abstract
Analysis of continuous-time piecewise linear systems based on piecewise quadratic (PWQ) Lyapunov functions typically requires continuity of these functions. Several conditions for guaranteeing continuity of PWQ functions over state-space partitions can be found in the literature. In this technical note, we show that these continuity conditions are equivalent over so-called simplicial conic partitions. As a consequence, the choice of which condition to impose can be based solely on practical considerations such as specific application or numerical aspects, without introducing additional conservatism in the analysis.
Fields of Study & Subjects
Mathematics and Applications
Graph theory and applications
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- IEEE Transactions on Automatic Control
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Volume
- 71
- Issue
- 7
- Pages
- 4732–4739
- Publication date
- 20 January 2026
- Language
- EN