Almost sure state estimation for nonlinear stochastic systems with Markovian switching

In this paper, the almost sure asymptotic stability is investigated for the state estimation problem of a general class of nonlinear stochastic systems with Markovian switching. A nonlinear state estimator with Markovian switching is first proposed, and then, a sufficient condition is given, which g...

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Bibliographic Details
Published in:Nonlinear dynamics 2014-04, Vol.76 (2), p.1591-1602
Main Authors: Kan, Xiu, Shu, Huisheng, Li, Zhenna
Format: Article
Language:English
Subjects:
Asymptotic properties
Automotive Engineering
Classical Mechanics
Control
Control systems
Dynamic stability
Dynamical Systems
Engineering
Estimating techniques
Liapunov functions
Markov analysis
Markov processes
Mechanical Engineering
Nonlinear dynamics
Nonlinear systems
Nonlinearity
Original Paper
Stability
State estimation
Stochastic systems
Switching
Vibration
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Summary:In this paper, the almost sure asymptotic stability is investigated for the state estimation problem of a general class of nonlinear stochastic systems with Markovian switching. A nonlinear state estimator with Markovian switching is first proposed, and then, a sufficient condition is given, which guarantees the almost sure asymptotic stability of the dynamics of the estimation error. Based on this condition, some simplified criteria are deduced by taking special forms of Lyapunov functions. Subsequently, an easy-to-verify procedure is put forward for the state estimation problem of the linear stochastic system with Markovian switching. Finally, two numerical examples are used to illustrate the effectiveness of the main results.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-013-1231-y