Regional Stability Analysis of Discrete-Time Piecewise Affine Systems
In this article, we study the regional stability of discrete-time piecewise affine (PWA) systems. The proposed method for the stability analysis uses an implicit representation of PWA systems based on ramp functions, and it builds upon Linear Matrix Inequalities to verify the nonnegativity of piecewise quadratic (PWQ) functions in a given set. Verifying the nonnegativity of PWQ functions allows us to solve Lyapunov inequalities yielding a PWQ Lyapunov function of which a level set gives an estimate of the region of attraction of the origin. Numerical results illustrate the effectiveness of the proposed method.
Authors
- Leonardo Cabral (ORCID: https://orcid.org/0000-0002-3331-1337)
- J.M. Gomes da Silva (ORCID: https://orcid.org/0000-0002-6275-2895)
- Giórgio Valmórbida (ORCID: https://orcid.org/0000-0002-1710-8590)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Universidade Federal do Rio Grande do Sul (BR)
- Laboratoire des signaux et systèmes (FR)
- CentraleSupélec (FR)
Publication Details
- Journal
- IEEE Transactions on Automatic Control
- Published
- 2024-10-25
- DOI
- https://doi.org/10.1109/tac.2024.3486656
- Citations
- 1
- Primary Topic
- Stability and Control of Uncertain Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.33