Finite-time stability theorem of stochastic nonlinear systems
A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Itô differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary ar...
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| Published in | Automatica (Oxford) Vol. 46; no. 12; pp. 2105 - 2108 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Ltd
01.12.2010
Elsevier |
| Subjects | |
| Online Access | Get full text |
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| Abstract | A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Itô differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions. Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper. |
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| AbstractList | A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Ito differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions. Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper. A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Itô differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions. Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper. |
| Author | Chen, Weisheng Jiao, L.C. |
| Author_xml | – sequence: 1 givenname: Weisheng surname: Chen fullname: Chen, Weisheng email: wshchen@126.com organization: Department of Applied Mathematics, Xidian University, Xi’an, 710071, PR China – sequence: 2 givenname: L.C. surname: Jiao fullname: Jiao, L.C. email: jlc1023@163.com organization: Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Institute of Intelligent Information Processing, Xidian University, Xi’an, 710071, PR China |
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| Keywords | Lyapunov method Stochastic settling time function Finite-time stability Stochastic nonlinear systems Itô equation Stability Probabilistic approach Differential equation Non linear control Non linear system Uncertain system Non deterministic system Lyapunov function |
| Language | English |
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| Snippet | A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by... |
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| SubjectTerms | Applied sciences Computer science; control theory; systems Control system analysis Control theory. Systems Differential equations Dynamical systems Exact sciences and technology Finite-time stability Lyapunov functions Lyapunov method Nonlinear dynamics Stability Stochastic nonlinear systems Stochastic settling time function Stochastic systems Stochasticity Theorems |
| Title | Finite-time stability theorem of stochastic nonlinear systems |
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