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Stabilization of Markov jump linear systems using quantized state feedback

2010; Elsevier BV; Volume: 46; Issue: 10 Linguagem: Inglês

10.1016/j.automatica.2010.06.018

1873-2836

Nan Xiao, Lihua Xie, Minyue Fu,

Neural Networks Stability and Synchronization

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.