Asymptotic stability of a class of nonlinear stochastic systems undergoing Markovian jumps
| Autor: | R.H. Huan, W.Q. Zhu, F. Ma, Z.G. Ying |
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| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Aerospace Engineering Ocean Engineering 02 engineering and technology Lyapunov exponent Civil Engineering Mathematical Sciences Hamiltonian system Stochastic stability symbols.namesake 020901 industrial engineering & automation Engineering 0203 mechanical engineering Exponential stability Control theory Linearization Stability theory Applied mathematics Civil and Structural Engineering Mathematics Mechanical Engineering Quasi-nonintegrable Hamiltonian Lyapunov exponents Statistical and Nonlinear Physics Condensed Matter Physics Nonlinear system Stability conditions 020303 mechanical engineering & transports Nuclear Energy and Engineering Markovian jumps Stochastic averaging symbols Hamiltonian (quantum mechanics) |
| Zdroj: | Huan, RH; Zhu, WQ; Ma, F; & Ying, ZG. (2016). Asymptotic stability of a class of nonlinear stochastic systems undergoing Markovian jumps. Probabilistic Engineering Mechanics, 45, 13-21. doi: 10.1016/j.probengmech.2016.02.005. UC Berkeley: Retrieved from: http://www.escholarship.org/uc/item/6z6920xx |
| DOI: | 10.1016/j.probengmech.2016.02.005. |
| Popis: | © 2016 Elsevier Ltd. All rights reserved. Systems which specifications change abruptly and statistically, referred to as Markovian-jump systems, are considered in this paper. An approximate method is presented to assess the asymptotic stability, with probability one, of nonlinear, multi-degree-of-freedom, Markovian-jump quasi-nonintegrable Hamiltonian systems subjected to stochastic excitations. Using stochastic averaging and linearization, an approximate formula for the largest Lyapunov exponent of the Hamiltonian equations is derived, from which necessary and sufficient conditions for asymptotic stability are obtained for different jump rules. In a Markovian-jump system with unstable operating forms, the stability conditions prescribe limitations on time spent in each unstable form so as to render the entire system asymptotically stable. The validity and utility of this approximate technique are demonstrated by a nonlinear two-degree-of-freedom oscillator that is stochastically driven and capable of Markovian jumps. |
| Databáze: | OpenAIRE |
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