Quantized stabilization of Markov jump linear systems via state feedback

  • Authors:

  • Nan Xiao;Lihua Xie;Minyue Fu

  • Affiliations:

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

  • Venue:
  • ACC'09 Proceedings of the 2009 conference on American Control Conference
  • Year:
  • 2009

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Abstract

This paper addresses the quantized stabilization problem for single-input Markov jump systems. Mode-dependent and mode-independent quadratic control Lyapunov functions based on the availability of mode information at controller/quantizer are considered for the quantized feedback. Similar to the linear time-invariant case, it is shown that a mode-dependent (respectively, mode-independent) logarithmic quantizer is optimal (coarsest) in the mean square quadratic stability (respectively, strongly mean square quadratic stability) sense for Markov jump systems. Moreover, the sector bound approach is shown to be nonconservative in investigating the corresponding quantized state feedback problem. Under an appropriate definition of quantization coarseness, we also present a method of optimal quantizer design in terms of linear matrix inequalities. Several examples including applications in networked control systems are given to demonstrate the results.