Premium
Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays
Author(s) -
Hu Zhipei,
Deng Feiqi,
Shi Peng,
Luo Shixian,
Xing Mali
Publication year - 2018
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.4077
Subject(s) - control theory (sociology) , probabilistic logic , exponential stability , network packet , stability (learning theory) , mathematical optimization , exponential function , controller (irrigation) , probability distribution , computer science , quantization (signal processing) , upper and lower bounds , mathematics , control (management) , algorithm , statistics , computer network , mathematical analysis , physics , nonlinear system , quantum mechanics , machine learning , agronomy , artificial intelligence , biology
Summary This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.