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Quantization, time delays, and nonlinear stabilization

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1 Author(s)
Liberzon, D. ; Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA

The purpose of this note is to demonstrate that a unified study of quantization and delay effects in nonlinear control systems is possible by merging the quantized feedback control methodology recently developed by the author and the small-gain approach to the analysis of functional differential equations with disturbances proposed earlier by Teel. We prove that under the action of a robustly stabilizing feedback controller in the presence of quantization and time delays satisfying suitable conditions, solutions of the closed-loop system starting in a given region remain bounded and eventually enter a smaller region. We present several versions of this result and show how it enables global asymptotic stabilization via a dynamic quantization strategy.

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Automatic Control, IEEE Transactions on  (Volume:51 ,  Issue: 7 )