Stabilization of Hybrid Systems by Feedback Control Based on Discrete-Time State Observations

You, Surong; Liu, Wei; Lu, Jianqiu; Mao, Xuerong; Qiu, Qinwei

doi:10.1137/140985779

Cited by 149 publications

(122 citation statements)

References 27 publications

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“…Due to the general techniques used in proofs in [16], the τ was required to be quite small in that paper. Mao and his group, therefore, modified the techniques and released the restriction on τ in [26,27]. We further observe that various effects, such as data transmission, may be time consuming.…”

Section: D(x(t)) = (F (X(t) R(t) T) + U(x(t) R(t) T))dt + G(x(t)mentioning

confidence: 92%

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Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

Qiu

Liu

et al. 2016

Statistics & Probability Letters

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Feedback control based on discrete-time state observation for stochastic differential equations with Markovian switching was initialled by Mao (2013). In practice, various effects could cause some time delay in the control function. Therefore, the time delay is taken into account for the discrete-time state observation in this paper and the mean-square exponential stability of the controlled system IS investigated.This paper is devoted as a continuous research to Mao (2013).

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Section: D(x(t)) = (F (X(t) R(t) T) + U(x(t) R(t) T))dt + G(x(t)mentioning

confidence: 92%

“…There are some available computer software, such as Matlab, for step 2, and the ideas for step 1 have been discussed in [26]. So we omit it here.…”

Section: Simumentioning

confidence: 99%

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

Qiu

Liu

et al. 2016

Statistics & Probability Letters

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“…However, this is possible in our case and we will show this under the same conditions of Theorem 5.1 without any additional condition, unlike Theorem 5.2 which needs the additional condition (5.3). We should also point out that You et al [28] showed lim t\rightar\infty | x(t)| = 0 a.s. from E \int \infty 0 | x(t)| 2 dt < \infty (please note it is 2 but not q) under the linear growth condition. Our new proof given below not only overcomes the difficulty without the linear growth condition but is also much simplified.…”

Section: R(t))db(t)mentioning

confidence: 84%

“…On the other hand, You et al [28] showed this is possible if both coefficients f and g of the SDDE (4.1) satisfy the linear growth condition. However, we are interested in the SDDEs which do not satisfy the linear growth condition in this paper.…”

Section: R(t))db(t)mentioning

confidence: 99%

Structured Robust Stability and Boundedness of Nonlinear Hybrid Delay Systems

Fei¹,

Hu²,

Mao³

et al. 2018

SIAM J. Control Optim.

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Abstract. Taking different structures in different modes into account, the paper has developed a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations (SDDEs) without the linear growth condition. A new Lyapunov function is designed in order to deal with the effects of different structures as well as those of different parameters within the same modes. Moreover, a lot of effort is put into showing the almost sure asymptotic stability in the absence of the linear growth condition. 1. Introduction. Systems in many branches of science and industry not only depend on the present state and the past ones but may also experience abrupt changes in their structures and parameters. Hybrid stochastic differential delay equations (SDDEs; also known as SDDEs with Markovian switching) have been widely used to model these systems (see, e.g., the books [23,24] and the references therein). One of the important issues in the study of hybrid SDDEs is the asymptotic analysis of stability and boundedness (see, e.g., [3,5,13,19]). In asymptotic analysis, robust stability and boundedness have been two of most popular topics. For example, Ackermann [1] gave a nice motivation of robust stability. Hinrichsen and Pritchard [7,8] presented an excellent discussion of the stability radii of linear systems with structured perturbations. Su [26] and Tseng, Fong, and Su [27] discussed robust stability for linear delay equations. In the aspect of robustness of stochastic stability, Haussmann [6] studied robust stability for a linear system and Ichikawa [11] for a semilinear system. Mao, Koroleva, and Rodkina [21] discussed the robust stability of uncertain linear or semilinear stochastic delay systems. Mao [20] investigated the stability of the stochastic delay interval system with Markovian switching. For more information on the stability and boundedness of hybrid SDDEs, please see, e.g., [12,22,23,25]. However, all of the papers, up to 2013, in this area only considered these robust

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“…However, due to the existence of zero‐order holder, the sampled‐data controller holding the control signal constant during the sampling period introduces discontinuity to the systems that complicates dynamic behaviors of systems and makes the analysis and control design more difficult. In recent years, sampled‐data control has been received increasing attentions in the control field . In the literature, there are three main approaches for sampled‐data control design for nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

Qi-xu

2017

Intl J Robust & Nonlinear

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Summary In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

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Stabilization of Hybrid Systems by Feedback Control Based on Discrete-Time State Observations

Cited by 149 publications

References 27 publications

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay

Structured Robust Stability and Boundedness of Nonlinear Hybrid Delay Systems

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

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