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In this chapter, we mainly study the finite-time and fixed-time control problems of differential equations with discontinuous state on the right-hand side. Under the framework of Filippov solution, we derive some general sufficient conditions to guarantee the global existence of the solutions to systems with discontinuous activation functions and various delays. By designing different controllers and applying some new analysis techniques, some novel Lyapunov Krasovskii functionals are constructed, and sufficient conditions to ensure finite-time or fixed-time synchronization are obtained.

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Finite-Time and Fixed-Time Control of Differential Equations with Discontinuous State

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  • 发表日期：

    2025年

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  • Xinsong Yang,
  • Yaping Sun,
  • Rongqiang Tang,
  • Meijie Zhang

摘要

In this chapter, we mainly study the finite-time and fixed-time control problems of differential equations with discontinuous state on the right-hand side. Under the framework of Filippov solution, we derive some general sufficient conditions to guarantee the global existence of the solutions to systems with discontinuous activation functions and various delays. By designing different controllers and applying some new analysis techniques, some novel Lyapunov Krasovskii functionals are constructed, and sufficient conditions to ensure finite-time or fixed-time synchronization are obtained.