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access icon free Separable Lyapunov-like functions for switched positive non-linear systems via a contractive approach

  • Author(s): Qian Liu 1, 2
    • View affiliations
  • Source: Volume 13, Issue 7, 30 April 2019, p. 943 – 951
    DOI:  10.1049/iet-cta.2018.5206 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 19/04/2018, Accepted 18/01/2019, Revised 12/12/2018, Published 23/01/2019

This study presents a result on constructing separable Lyapunov-like functions for the switched positive non-linear system. Firstly, the contraction theory has been introduced to the stability analysis of the switched positive non-linear system. Secondly, the specific forms of a set of separable Lyapunov-like functions have been demonstrated for stable subsystems and unstable subsystems to achieve the asymptotic stability for any switching signal satisfying an average dwell time constraint. Additionally, an algorithm is provided to compute the set of separable Lyapunov-like functions based on the sum of squares programming. Finally, three simulation examples are provided to illustrate the effectiveness of their result.

Inspec keywords: control system synthesis; time-varying systems; linear systems; Lyapunov methods; stability; asymptotic stability; nonlinear control systems

Other keywords: nonlinear system; contraction theory; switching signal; contractive approach; switched positive nonlinear systems; separable Lyapunov-like functions

Subjects: Nonlinear control systems; Control system analysis and synthesis methods; Linear control systems; Stability in control theory

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