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Asymptotic stabilization of dynamically quantized nonlinear systems in feedforward form
Received:September 7,2009  Revised:September 7,2009
Keywords:Quantization  Stability  Nonlinear  Feedforward.
Fund Project:the National Natural Science Foundation of China (No.60904012), the Natural Science Foundation of Anhui Province(No.090412050) and the Talent Development Program of Anhui Province (No.2008Z012).
Qiang LIMG University of Science and Technology of China qling@ustc.edu.cn 
Michael D. LEMMON University of Notre Dame  
Hai LIN National University of Singapore  
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      This paper studies the stabilizability of an n-dimensional quantized feedforward nonlinear system. The state of that system is first quantized into a finite number of bits, and then sent through a digital network to the controller. We want to minimize the number of transmitted bits subject to maintaining asymptotic stability. In the prior literature, n bits are used to stabilize the n-dimensional system by assigning one bit to each state variable (dimension). Under the stronger assumption of global Lipschitz continuity, this paper extends that result by stabilizing the system with a single bit. Its key contribution is a dynamic quantization policy which dynamically assigns the single bit to the most important state variable. Under this policy, the quantization error exponentially converges to 0 and the stability of the system can, therefore, be guaranteed. Because 1 is the minimum number of quantization bits (per sampling step), the proposed dynamic quantization policy achieves the minimum stabilizable bit number for that n-dimensional feedforward nonlinear system.
Qiang LING,Michael D. LEMMON and Hai LIN.Asymptotic stabilization of dynamically quantized nonlinear systems in feedforward form[J].Journal of Control Theory and Applications,2010,8(1):27~33.
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