Robust Control of Implicit Systems

  • Alexander Poznyak
  • Andrey Polyakov
  • Vadim Azhmyakov
Part of the Systems & Control: Foundations & Applications book series (SCFA)


This chapter deals with a new approach to robust control design for a class of nonlinearly affine control systems. The dynamic models under consideration are described by implicit differential equations in the presence of additive bounded uncertainties. The proposed robust feedback design procedure is based on an extended version of the classical invariant ellipsoid technique. In this book, this extension is called the attractive ellipsoid method. The stability/robustness analysis of the resulting closed-loop system involves a modified descriptor approach associated with the usual Lyapunov-type methodology. The theoretical schemes elaborated in our contribution are finally illustrated by a simple computational example.


Implicit systems Sampled-data systems Attractive ellipsoids 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexander Poznyak
    • 1
  • Andrey Polyakov
    • 2
  • Vadim Azhmyakov
    • 3
  1. 1.Automatic Control DepartmentCentro de Investigacion y Estudios AvanzadosMéxicoMexico
  2. 2.Non-AINRIA-LNEVilleneuve d’AscqFrance
  3. 3.Faculty of Electronic and Biomedical EngineeringUniversity of Antonio NariñoNeivaColombia

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