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On Diagonal Stability of Positive Systems with Switches and Delays

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Abstract

We consider linear positive systems with delay and switchings of operation modes. We establish conditions under which it is possible to construct a common Lyapunov–Krasovskii diagonal functional for the family of subsystems corresponding to the system with switchings in consideration. These conditions are formulated in terms of the feasibility of auxiliary systems of linear algebraic inequalities. In addition, we study the problem of the existence of a diagonal functional of a special form. We also show that our results can be used to analyze the stability of some classes of nonlinear positive systems with delay.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. Yu. Aleksandrov

  2. ITMO University (National Research University of Information Technologies, Mechanics and Optics), St. Petersburg, Russia

    A. Yu. Aleksandrov

  3. National University of Ireland, Maynooth, Ireland

    O. Mason

  4. Irish Software Research Centre Lero, Limerick, Ireland

    O. Mason

Authors
  1. A. Yu. Aleksandrov
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  2. O. Mason
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Correspondence to A. Yu. Aleksandrov.

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Original Russian Text © A.Yu. Aleksandrov, O. Mason, 2018, published in Avtomatika i Telemekhanika, 2018, No. 12, pp. 16–33.

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Aleksandrov, A.Y., Mason, O. On Diagonal Stability of Positive Systems with Switches and Delays. Autom Remote Control 79, 2114–2127 (2018). https://doi.org/10.1134/S0005117918120020

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  • DOI: https://doi.org/10.1134/S0005117918120020

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