Stabilization of Markov jump linear systems using quantized state feedback

This paper addresses the stabilization problem for single-input Markov jump linear systems via modedependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and amode-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. © 2010 Elsevier Ltd. All rights reserved.