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Stability of Reset Control Systems

  • Alfonso BañosEmail author
  • Antonio Barreiro
Part of the Advances in Industrial Control book series (AIC)

Abstract

This chapter presents results on the stability of reset control systems with finite-dimensional base systems. The stability problem is addressed from different, complementary points of view: (i) internal or Lyapunov stability, (ii) external or input–output stability with passivity analysis, and (iii) stability by the describing function method. Internal stability techniques are subdivided into techniques giving rise to stability conditions that do not depend directly on the reset instants (reset-times independent) or, alternatively, are reset-times dependent. The first case is obtained directly using continuous time Lyapunov functions (that gives rise to the so-called H β condition), while the second case (reset-times dependent) requires a discretization at the after-reset values and a subsequent discrete-time Lyapunov analysis. Then, the input–output Open image in new window stability is studied, and a number or results are presented in connection with passivity and dissipativity properties of reset feedback loops. Finally, the standard describing function tool is used for approximately predicting the appearance or absence of oscillations and as a good practical tool to evaluate the phase lead obtained by reset compensation. The material is based on several published works (Baños et al. in European Control Conference, Kos, Greece, 2007; Baños et al. in Proc. IEEE International Symposium on Industrial Electronics, Spain, 2007; Baños et al. in 3rd IFAC Conference on Analysis and Design of Hybrid Systems, Zaragoza, Spain, 2009; Baños et al. in Nonlinear Anal. Hybrid Syst., 2010, doi: 10.1016/j.nahs.2010.07.004; Baños et al. in IEEE Trans. Autom. Control 56(1):217–223, 2011; Carrasco et al. in 34th Annual Conference of the IEEE Industrial Electronics Society, Orlando, Florida, USA, 2008; Carrasco et al. in Syst. Control Lett. 59(1):18–24, 2010).

Keywords

Impulsive Differential Equation Phase Lead High Order Harmonic Compensator State Base Compensator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Fac. Informática, Depto. Informática y Sistemas, Grupo de Informática IndustrialUniversidad de MurciaMurciaSpain
  2. 2.Depto. Ingeniería de Sistemas y Automática, ETSIIUniversidad de VigoVigoSpain

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