This paper is concerned with mean-square stabilization of single-input Markovian jump linear systems (MJLSs) with logarithmically quantized state feedback. We introduce the concepts and provide explicit constructions of stabilizing mode-dependent logarithmic quantizers together with associated controllers, and a semi-convex way to determine the optimal (coarsest) stabilizing quantization density. An example application is presented as a special case of the developed framework, that of feedback stabilizing a linear time-invariant (LTI) system over a log-quantized erasure channel. A hardware implementation of this application on an inverted pendulum testbed is provided using a finite word-length approximation.
Stabilization of Markovian Jump Linear Systems With Log-Quantized Feedback
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 30, 2013; final manuscript received November 19, 2013; published online February 24, 2014. Assoc. Editor: Jongeun Choi.
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Xu, Q., Zhang, C., and Dullerud, G. E. (February 24, 2014). "Stabilization of Markovian Jump Linear Systems With Log-Quantized Feedback." ASME. J. Dyn. Sys., Meas., Control. May 2014; 136(3): 031019. https://doi.org/10.1115/1.4026133
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