Regulator problem for linear systems with constraints on control and its increment or rate

  • Authors:

  • Fouad Mesquine;Fernando Tadeo;Abdellah Benzaouia

  • Affiliations:

  • Faculty of Sciences, Physics Department, Research Unit Constrained and Robust Regulation, University Cadi Ayyad, P.O. Box 2390, Marrakesh 40000, Morocco;Departamento de Ingenieria de Sistemas y Automatica, Universidad de Valladolid, Valladolid 47005, Spain;Faculty of Sciences, Physics Department, Research Unit Constrained and Robust Regulation, University Cadi Ayyad, P.O. Box 2390, Marrakesh 40000, Morocco

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2004

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Abstract

This paper discusses the problem of constraints on both control and its rate or increment, for linear systems in state space form, in both the continuous and discrete-time domains. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate (for the continuous-time case), such that the system evolves respecting incremental or rate constraints. A pole assignment technique is then used to solve the inverse problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on both control and its increment or rate. An illustrative example shows the application of the method on the double integrator problem.