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New results on stability of singular stochastic Markov jump systems with state‐dependent noise
Author(s) -
Zhao Yong,
Zhang Weihai
Publication year - 2015
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.3401
Subject(s) - mathematics , uniqueness , stability (learning theory) , markov chain , noise (video) , state (computer science) , matrix (chemical analysis) , jump , mean square , discrete time and continuous time , markov process , representation (politics) , control theory (sociology) , mathematical optimization , computer science , mathematical analysis , algorithm , law , control (management) , statistics , physics , quantum mechanics , machine learning , artificial intelligence , image (mathematics) , materials science , composite material , politics , political science
Summary This paper aims to develop the stability theory for singular stochastic Markov jump systems with state‐dependent noise, including both continuous‐time and discrete‐time cases. The sufficient conditions for the existence and uniqueness of a solution to the system equation are provided. Some new and fundamental concepts such as non‐impulsiveness and mean square admissibility are introduced, which are different from those of other existing works. By making use of the ℋ ‐representation technique and the pseudo inverse E + of a singular matrix E , sufficient conditions ensuring the system to be mean square admissible are established in terms of strict linear matrix inequalities, which can be regarded as extensions of the corresponding results of deterministic singular systems and normal stochastic systems. Practical examples are given to demonstrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.