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Stability and Stabilization for Discrete System With Probabilistic Nonlinearities

[+] Author and Article Information
Xia Zhao

Nanjing College of Information Technology,
Nanjing, 210046, PRC

Engang Tian

School of Electrical and Automation Engineering,
Nanjing Normal University,
Nanjing 210042, China
e-mail: teg@njnu.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received May 3, 2012; final manuscript received March 6, 2013; published online June 25, 2013. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 135(5), 054502 (Jun 25, 2013) (4 pages) Paper No: DS-12-1125; doi: 10.1115/1.4024305 History: Received May 03, 2012; Revised March 06, 2013

This paper investigates stability and stabilization of discrete systems with probabilistic nonlinearities and time-varying delay. New characters of the nonlinearities, the probability of the nonlinearities happening between different bounds, are used to build new type of system model, which can help us make a full use of the inner variation information of the nonlinearities. With the help of the new characters, new system model is proposed. Then, sufficient conditions for the mean square stability of the system can be obtained by using the Lyapunov functional approach and linear matrix inequalities technique. An example is proposed to illustrate the efficiency of the proposed method.

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