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

Chaker Jammazi, Mohamed Boutayeb and Karima Saidi

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

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.

Keywords: Fixed-time/finite-time stability; Polynomial stability; Lyapunov design; Bilinear control systems; Double integrator; Output feedback (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007944

DOI: 10.1016/j.chaos.2023.113893

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