Regional Stability Analysis of Discrete-Time Piecewise Affine Systems

• 成果类型: Article
• 署名作者: Cabral, Leonardo; Valmorbida, Giorgio; da Silva Jr, Joao Manoel Gomes
• 署名单位: Universidade Federal do Rio Grande do Sul; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Inria; Universidade Federal do Rio Grande do Sul
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3486656
• 发表日期: 2025
• 页码: 2507-2520
• 关键词: trajectory; Stability criteria; Symmetric matrices; Numerical stability; vectors; Level set; system dynamics; Predictive control; optimization; mathematical models; Local stability analysis; piecewise affine (PWA) systems; piecewise quadratic (PWQ) functions

摘要

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.