Truncated predictor feedback for linear systems with long time-varying input delays

  • Authors:

  • Bin Zhou;Zongli Lin;Guang-Ren Duan

  • Affiliations:

  • Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, China;Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743-4743, Charlottesville, VA 22904-4743, USA;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin, 150001, China

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2012

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Abstract

In this paper we study the problem of stabilizing a linear system with a single long time-varying delay in the input. Under the assumption that the open-loop system is stabilizable and not exponentially unstable, a finite dimensional static time-varying linear state feedback controller is obtained by truncating the predictor based controller and by adopting the parametric Lyapunov equation based controller design approach. As long as the time-varying delay is exactly known and bounded, an explicit condition is provided to guarantee the stability of the closed-loop system. It is also shown that the proposed controller achieves semi-global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints. Numerical examples show the effectiveness of the proposed approach.