Prescribed-Time Stability of Nonlinear Impulsive Piecewise Systems and Synchronization for Dynamical Networks

• Lichao Feng ^[3] ; Chenchen Li ^[3] ; Mahmoud Abdel-Aty ^[1] ; Jinde Cao
  1. [1] Sohag University

     Sohag University

     Egipto

     
  2. [2] Southeast University

     Southeast University

     China

     
  3. [3] North China University of Science and Technology

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
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• Resumen

  • The previous work by Li et al. (Appl Math Model 115: 385–397, 2023) has investigated a prescribed-time stability result for impulsive piecewise-smooth systems, based on linear Lyapunov inequality (LLI) and time-varying piecewise-smooth function (TVPSF). Nevertheless, it should be noted that human-devised TVPSFs may not match with the dynamic characteristics of systems, and LLIs will exclude many nonlinear systems. Thus, it is of necessity to overcome these intractable constraints. Fortunately, this paper has done it. Motivated by these, based on two nonlinear Lyapunov inequalities (NLIs) without TVPSFs, two novel assertions on prescribed-time stability of nonlinear impulsive piecewise-smooth systems are established by the set-valued analysis technique. Furthermore, based on the two novel assertions above, two feedback controllers without TVPSFs are devised to achieve prescribed-time synchronization of impulsive piecewise-smooth dynamical networks by Lyapunov method. The proposed approach enables one to preset the settling time without being constrained by initial values and control parameters. Finally, two examples on chaotic Sprott circuits are imported to validate the obtained results.

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