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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).
AuthorInstitutionE-mail
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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Abstract:
      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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