Automation and Remote Control

, Volume 80, Issue 8, pp 1375–1389 | Cite as

Switched Systems, Lur’e Systems, Absolute Stability, Aizerman Problem

  • V. A. KamenetskiyEmail author
Nonlinear Systems


We distinguish a subclass of switched linear systems that we call pairwise connected. We show that the dynamics of such systems can be described by Lur’e systems. For pairwise connected systems, we obtain a sufficient frequency-domain condition for the existence of a quadratic Lyapunov function. The well-known Aizerman problem is reformulated for switched linear systems. We show an example of a system with switchings between three linear third order subsystems for which Aizerman’s problem has a positive solution.


switched systems Lur’e systems stability Aizerman problem Lyapunov functions matrix inequalities 


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This work was supported by the Program of the Presidium of the Russian Academy of Sciences “Modern Problems of Robotics,” project no. I.29.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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