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Finite‐Time Stability and Stabilization of Linear Itô Stochastic Systems with State and Control‐Dependent Noise
Author(s) -
Yan Zhiguo,
Zhang Guoshan,
Zhang Weihai
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.531
Subject(s) - control theory (sociology) , stability (learning theory) , mathematics , stochastic control , linear matrix inequality , controller (irrigation) , state (computer science) , matrix (chemical analysis) , full state feedback , noise (video) , linear system , mathematical optimization , computer science , control (management) , optimal control , mathematical analysis , algorithm , materials science , image (mathematics) , machine learning , artificial intelligence , agronomy , composite material , biology
In this paper, finite‐time stability and stabilization problems for a class of linear stochastic systems are studied. First, a new concept of finite‐time stochastic stability is defined for linear stochastic systems. Then, based on matrix inequalities, some sufficient conditions under which the stochastic systems are finite‐time stochastically stable are given. Subsequently, the finite‐time stochastic stabilization is studied and some sufficient conditions for the existence of a state feedback controller and a dynamic output feedback controller are presented by using a matrix inequality approach. An algorithm is given for solving the matrix inequalities arising from finite‐time stochastic stability (stabilization). Finally, two examples are employed to illustrate the results.