NDLI: Finite gain stabilization with logarithmic quantization

Content Provider	IEEE Xplore Digital Library
Author	Chun Zhang Dullerud, G.E.
Copyright Year	2007
Description	Author affiliation: Illinois Univ., Urbana (Chun Zhang)
Abstract	In this paper, we consider the finite-gain stabilization problem in the case where there is logarithmic quantization in the feedback loop; more specifically, we consider a scalar- input discrete-time linear time invariant (LTI) system in the presence of additive deterministic or stochastic external disturbances, with logarithmically quantized state measurements available. Assuming that finite lp gain from the input to the states is achievable when the feedback is not quantized (or in the stochastic case that the p $^{th}-moment$ is finite), we show that there exist feasible logarithmic quantizers such that these boundedness properties are preserved when the state feedback is quantized. The main contribution of this paper is to show that static memoryless logarithmic quantizer is sufficient for finite gain stabilization. The quantizer density only depends on the open-loop system parameters. In addition to the controller construction, we also give explicit bounds on the l $_{p}$ gain, and in the stochastic case, the p $^{th}$ -moment of the state.
Starting Page	3952
Ending Page	3957
File Size	205151
Page Count	6
File Format	PDF
ISBN	9781424414970
ISSN	01912216
DOI	10.1109/CDC.2007.4434983
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Quantization Control systems Stochastic systems State feedback Stochastic processes Asymptotic stability Open loop systems Communication system control Linear feedback control systems USA Councils
Content Type	Text
Resource Type	Article

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