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Zbl 1204.93127
Xiao, Nan; Xie, Lihua; Fu, Minyue
Stabilization of Markov jump linear systems using quantized state feedback. (English)
[J] Automatica 46, No. 10, 1696-1702 (2010). ISSN 0005-1098

Summary: 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.

MSC 2000:: *93E15 Stochastic stability
93C05 Linear control systems
93D15 Stabilization of systems by feedback
60J75 Jump processes
93B52 Feedback control

Keywords: Markov jump linear systems; mean square quadratic stability; networked control systems; quantized stabilization

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