A Contraction Theory Approach to Stochastic Incremental Stability
We investigate the incremental stability properties of Ito stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can...
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| Veröffentlicht in: | IEEE transactions on automatic control 2009-04, Vol.54 (4), p.816-820 |
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| container_title | IEEE transactions on automatic control |
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| creator | Quang-Cuong Pham Tabareau, N. Slotine, J.-J. |
| description | We investigate the incremental stability properties of Ito stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of nonlinear observers design and stochastic synchronization. |
| doi_str_mv | 10.1109/TAC.2008.2009619 |
| format | Article |
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Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of nonlinear observers design and stochastic synchronization.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2008.2009619</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Computer science; control theory; systems ; Control system analysis ; Control systems ; Control theory. 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Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of nonlinear observers design and stochastic synchronization.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Control system analysis</subject><subject>Control systems</subject><subject>Control theory. 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| ispartof | IEEE transactions on automatic control, 2009-04, Vol.54 (4), p.816-820 |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Computer science control theory systems Control system analysis Control systems Control theory. Systems Convergence Design engineering Dynamical systems Eigenvalues and eigenfunctions Exact sciences and technology Incremental stability Mean square values Modelling and identification nonlinear contraction theory Nonlinear dynamics Nonlinear systems Nonlinearity Stability Stability analysis Standards development Stochastic processes Stochastic resonance stochastic stability Stochastic systems Stochasticity Symmetric matrices Synchronization |
| title | A Contraction Theory Approach to Stochastic Incremental Stability |
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