Distance to Internal Instability of Linear Time-Invariant Systems Under Structured Perturbations

• 成果类型: Article
• 署名作者: Menini, Laura; Possieri, Corrado; Tornambe, Antonio
• 署名单位: University of Rome Tor Vergata; University of Rome Tor Vergata
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3004350
• 发表日期: 2021
• 页码: 1941-1956
• 关键词: Asymptotic stability; Linear systems; Robust control; Robustness

摘要

In this article, uncertain continuous-time and discrete-time linear time-invariant systems are considered. The uncertainties are assumed to affect polynomially the dynamics of the system and they can be structured. The problem of computing the distance to internal instability of an internally exponentially stable nominal system is solved by using tools from algebraic geometry, thus extending previous results valid in case of unstructured uncertainties. The choice of the nominal system is formulated and solved as the choice of a point in the parameter space that is sufficiently far from the boundary of the domain of stability. A simple example of application to robust control is outlined.