Finite-time stability and instability of stochastic nonlinear systems

Yin, Juliang; Khoo, Suiyang; Man, Zhihong; Yu, Xinghuo

doi:10.1016/j.automatica.2011.08.050

Cited by 417 publications

(224 citation statements)

References 24 publications

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“…However, these stability criteria fail when we want to know the behavior of the solution of a stochastic system in finite time. As a consequence, finite-time stability for stochastic systems has become popular in recent years (Chen & Jiao, 2010;Yang, Li, & Chen, 2009;Yin, Khoo, Man, & Yu, 2011). By using the state partition of continuous parts of systems, Yang et al (2009) designed a feedback controller to ensure that a nonlinear stochastic hybrid system is finite-time stochastically stable.…”

Section: Introductionmentioning

confidence: 99%

Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form

2015

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Section: Introductionmentioning

confidence: 99%

Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form

2015

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“…then the filtering problem for system (1) is solved by (5) in the sense of asymptotic stability in probability.…”

Section: Now We Have Proved Thatmentioning

confidence: 99%

“…The H ∞ filtering has been extensively studied to guarantee that the L 2 gain from the disturbance to the estimation error is less than a predefined positive level [3,4]. For stochastic systems, the concept of stability in probability is important [5,6] because it can describe the system dynamics in a probabilistic way. So far, the filtering problem in the sense of stability in probability has stirred some initial research interests [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

filtering for non‐linear systems with stochastic sensor saturations and Markov time delays: the asymptotic stability in probability

Liu

Wang

et al. 2016

IET Control Theory & Applications

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This paper is concerned with the filtering problem for a class of nonlinear systems with stochastic sensor saturations and Markovian measurement transmission delays, where the asymptotic stability in probability is considered. The sensors are subject to random saturations characterized by a Bernoulli distributed sequence. The transmission time-delays are governed by a discrete-time Markov chain with finite states. In the presence of the nonlinearities, stochastic sensor saturations and Markovian time-delays, sufficient conditions are established to guarantee that the filtering process is asymptotically stable in probability without disturbances and also satisfies the H ∞ criterion with respect to nonzero exogenous disturbances under the zero-initial condition. Moreover, it is illustrated that the results can be specialized to linear filters. Two simulation examples are presented to show the effectiveness of the proposed algorithms.

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“…Lemma [44]: Assume that a continuous, positive-definite function ) (t V satisfies the following differential inequality: …”

Section: Preliminariesmentioning

confidence: 99%

“…Moreover, the finite-time control techniques have demonstrated better robustness and disturbance rejection properties. Based on proposed fractional controllers, the finite-time stability and the settling time can be guaranteed and computed [37][38][39][40][41][42][43][44][45][46][47][48][49]. However, few studies have focused on the finite-time suppression chaos of permanent magnet synchronous motor (PMSM) systems.…”

Section: Introductionmentioning

confidence: 99%