Brief paper: Stabilization of Markov jump linear systems using quantized state feedback

  • Authors:

  • Nan Xiao;Lihua Xie;Minyue Fu

  • Affiliations:

  • School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore;School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW 2308, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2010

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Abstract

This paper addresses the stabilization problem for single-input Markov jump linear systems via mode-dependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and a mode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results for linear time-invariant systems. The sector bound approach is shown to be non-conservative in investigating the corresponding quantized state feedback problem, and then a method of optimal quantizer/controller design in terms of linear matrix inequalities is presented. Moreover, when the mode process is not observed by the controller and quantizer, a mode estimation algorithm obtained by maximizing a certain probability criterion is given. Finally, an application to networked control systems further demonstrates the usefulness of the results.