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On the fixed-time extinction based nonlinear control and systems decomposition: applications to bilinear systems

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  • Jammazi, Chaker
  • Boutayeb, Mohamed
  • Saidi, Karima

Abstract

This paper deals with new criteria of the fixed-time extinction of nonlinear dynamical systems. We show, by comparison principal, that Gronwall-like integral inequalities leading to the extinction of the energy system in fixed-time; this helps us to build fixed-time stabilizing feedback laws for bilinear control systems in Hilbert space. In addition, in order to relax some existing results on the fixed-time stability of systems by Lyapunov function, we prove that the decomposition of the system into two subsystems so that one is finite-time stable and the other is polynomially stable, leads to fixed-time extinction of the whole system. Our results are applied to the double integrator where new fixed-time stabilizing feedbacks, with various aspects, are constructed.

Suggested Citation

  • Jammazi, Chaker & Boutayeb, Mohamed & Saidi, Karima, 2023. "On the fixed-time extinction based nonlinear control and systems decomposition: applications to bilinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007944
    DOI: 10.1016/j.chaos.2023.113893
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    1. Jammazi, Chaker & Boutayeb, Mohamed & Bouamaied, Ghada, 2021. "On the global polynomial stabilization and observation with optimal decay rate," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
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