Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE

Yan Zhang, D. Subbaram Naidu, Chenxiao Cai, Yun Zou

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9 Scopus citations

Abstract

In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.

Original languageEnglish (US)
Pages (from-to)2632-2641
Number of pages10
JournalInternational Journal of Systems Science
Volume47
Issue number11
DOIs
StatePublished - Aug 17 2016

Keywords

  • Asymptotically stability
  • Composite control
  • Discrete-time nonlinear singularly perturbed systems
  • Optimal control
  • State-dependent Riccati equation

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