具有任意控制集的二阶线性切换系统：稳定性和不变范数

IF 2.6 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

European Journal of Control Pub Date : 2025-09-01 DOI:10.1016/j.ejcon.2025.101346

Vladimir Yu. Protasov , Asiiat Musaeva

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引用次数: 0

摘要

我们证明了平面线性开关系统的稳定性问题和构造Barabanov范数问题可以用显式形式解决。这对于每一个2 × 2矩阵的紧化控制集都可以做到。如果控制集不包含具有实谱的支配矩阵，则不变范数总是唯一的（直到乘子）并且属于C1。否则，可能有无限多个这样的范数，包括非光滑范数。所有这些都可以找到并分类。特别地，每一个对称凸体都是一个合适的线性交换系统的Barabanov范数的单位球。

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Second-order linear switching systems with arbitrary control sets: Stability and invariant norms

We show that the stability problem and the problem of constructing Barabanov norms can be resolved for planar linear switching systems in an explicit form. This can be done for every compact control set of 2 × 2 matrices. If the control set does not contain a dominant matrix with a real spectrum, then the invariant norm is always unique (up to a multiplier) and belongs to

C^{1}

. Otherwise, there may be infinitely many such norms, including non-smooth ones. All of them can be found and classified. In particular, every symmetric convex body is a unit ball of the Barabanov norm of a suitable linear switching system.

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来源期刊

European Journal of Control 工程技术-自动化与控制系统

CiteScore

5.80

自引率

5.90%

发文量

131

审稿时长

1 months

期刊介绍： The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field. The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering. The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications. Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results. The design and implementation of a successful control system requires the use of a range of techniques: Modelling Robustness Analysis Identification Optimization Control Law Design Numerical analysis Fault Detection, and so on.