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Quantized stabilization for stochastic discrete‐time systems with multiplicative noises
Author(s) -
Wei Li,
Zhang Huanshui,
Fu Minyue
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2778
Subject(s) - multiplicative function , mathematics , logarithm , multiplicative noise , control theory (sociology) , quantization (signal processing) , algebraic riccati equation , quadratic equation , stochastic control , riccati equation , linear system , optimal control , computer science , mathematical optimization , control (management) , algorithm , differential equation , mathematical analysis , geometry , signal transfer function , digital signal processing , artificial intelligence , analog signal , computer hardware
SUMMARY This paper considers the problem of quadratic mean‐square stabilization of a class of stochastic linear systems using quantized state feedback. Different from the previous works where the system is restricted to be deterministic, we focus on stochastic systems with multiplicative noises in both the system matrix and the control input. A static quantizer is used in the feedback channel. It is shown that the coarsest quantization density that permits stabilization of a stochastic system with multiplicative noises in the sense of quadratic mean‐square stability is achieved with the use of a logarithmic quantizer, and the coarsest quantization density is determined by an algebraic Riccati equation, which is also the solution to a special stochastic linear control problem. Our work is then extended to exponential quadratic mean‐square stabilization of the same class of stochastic systems. Copyright © 2011 John Wiley & Sons, Ltd.