General Formula for Event-Based Stabilization of Nonlinear Systems with Delays in the State

  • Sylvain Durand
  • Nicolas Marchand
  • J. Fermi Guerrero-Castellanos
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 6)


In this chapter, a universal formula is proposed for event-based stabilization of nonlinear systems affine in the control and with delays in the state. The feedback is derived from the seminal law proposed by E. Sontag (1989) and then extended to event-based control of affine nonlinear undelayed systems. Under the assumption of the existence of a control Lyapunov–Krasovskii functional (CLKF), the proposal enables smooth (except at the origin) asymptotic stabilization while ensuring that the sampling intervals do not contract to zero. Global asymptotic stability is obtained under the small control property assumption. Moreover, the control can be proved to be smooth anywhere under certain conditions. Simulation results highlight the ability of the proposed formula. The particular linear case is also discussed.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Sylvain Durand
    • 1
  • Nicolas Marchand
    • 2
  • J. Fermi Guerrero-Castellanos
    • 3
  1. 1.ICube, INSA StrasbourgUniversity of Strasbourg, CNRS (UMR 7357)StrasbourgFrance
  2. 2.GIPSA-LabUniversity of Grenoble Alpes, CNRS (UMR 5216)GrenobleFrance
  3. 3.Faculty of ElectronicsAutonomous University of Puebla (BUAP)PueblaMexico

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