Set-Theoretical Stability Analysis of LPV Systems via Minkowski-Lyapunov Functions

• 成果类型: Article
• 署名作者: Gallegos, Javier A.; Barbosa, Karina A.
• 署名单位: Pontificia Universidad Catolica de Chile; Universidad de Santiago de Chile
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3441325
• 发表日期: 2025
• 页码: 573-578
• 关键词: Stability criteria; Lyapunov methods; asymptotic stability; CONVERGENCE; Sufficient conditions; control theory; uncertainty; linear parameter-varying (LPV) systems; robust positive invariance; STABILITY

摘要

A set-theoretical approach based on Minkowski-Lyapunov functions is proposed to study the stability of polytopic systems in the linear parameter-varying (LPV) form. In contrast to the one based on quadratic Lyapunov functions, the proposed approach provides necessary and sufficient conditions for stability in both discrete and continuous time. Remarkably, the resulting conditions are computationally tractable and can be verified using algorithms with guaranteed convergence, in contrast to other set-theoretical tools. In addition, the proposed method is shown to be flexible enough to incorporate knowledge of the system, such as restrictions on the rate of variation of the parameters or the kind of disturbances and/or unmodeled dynamics encompassed, allowing to establish nonconservative robust stability conditions. Two illustrative examples are added to show the main advantages.