Sliding mode control with bounded <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>ℒ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> gain performance of Markovian jump singular time-delay systems

Wu, Ligang; Su, Xiaojie; Shi, Peng

doi:10.1016/j.automatica.2012.05.064

Cited by 478 publications

(271 citation statements)

References 11 publications

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“…To use our new theory, we need to know how to design the control function u : R n × S × R + → R n such that the hybrid SDE (10) is mean-square exponentially stable, namely Assumption 2 is satisfied. There is an intensive literature in the area of stability of hybrid SDEs, for example, [5,11,13,19,20]. For the convenience of the reader, we state a lemma which follows easily from [14, Thereom 4.5 on page 166].…”

Section: Case Studiesmentioning

confidence: 99%

“…[18]). For further references on hybrid SDEs, we mention, for example, [5,12,15,17,20]). In particular, [8] is one of most cited papers (more than 550 Google citations) while [14] is the first book in this area (more than 800 Google citations).…”

Section: Introductionmentioning

confidence: 99%

“…Instead of using a classical continuoustime feedback control u(x(t), r(t), t) which requires continuous observations of the state x(t) for all time t ≥ 0 (see e.g. [5,11,13,19,20]), Mao proposed in [10] to design a feedback control u(x(δ(t, t 0 , τ )), r(t), t) based on the discrete-time observations of the state in order to make the controlled system…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilisation of hybrid stochastic differential equations by feedback control based on discrete‐time observations of state and mode

Song

Zheng

Luo

et al. 2017

IET Control Theory & Applications

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This version is available at https://strathprints.strath.ac.uk/58494/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. (SDEs) by the feedback controls based on the discrete-time observations of the state. However, the feedback controls still depend on the continuous-time observations of the mode. Of course this is perfectly fine if the mode of the system is obvious (i.e. fully observable at no cost). However, it could often be the case where the mode is not obvious and it costs to identify the current mode of the system. To reduce the control cost, it is reasonable we identify the mode at the discrete times when we make observations for the state. Hence the feedback control should be designed based on the discrete-time observations of both state and mode. The aim of this paper is to show how to design such a feedback control to stabilise a given hybrid SDE. Stabilisation of Hybrid Stochastic Differential Equations by Feedback Control based on Discrete-time Observations of State and Mode

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Section: Case Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stabilisation of hybrid stochastic differential equations by feedback control based on discrete‐time observations of state and mode

Song

Zheng

Luo

et al. 2017

IET Control Theory & Applications

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“…Recently, sliding mode control has been studied for either T-S fuzzy descriptor systems [30] or Markovian jump descriptor systems [31,32,33]. There are, however, interesting issues outstanding.…”

Section: Introductionmentioning

confidence: 99%

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

Zhang

Yan

et al. 2017

IET Control Theory & Applications

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This paper investigates integral sliding mode control problems for Markovian jump T-S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analyzed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed.

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“…In Fei et al (2009), a new delay-dependent stochastic stability criterion for a class of MJSs with time delay was derived based on a novel Lyapunov-Krasovskii functional ap-proach. In Wu et al (2012), the problem on the sliding mode control of Markov jump singular time-delay systems is concerned through investigation of the bounded gain performance in the analysis of sliding mode dynamics in order to improve the system transient performance. Recently in Karimi (2011), an efficient approach is developed for robust H ∞ control problem of uncertain time-delay systems with Markovian switching parameters and mixed discrete, neutral and distributed delays.…”

Section: Introductionmentioning

confidence: 99%

tochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems

Wang¹,

Shi²,

Karimi³

et al. 2012

MIC

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In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the systems transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.

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Sliding mode control with bounded ℒ2 gain performance of Markovian jump singular time-delay systems

Cited by 478 publications

References 11 publications

Stabilisation of hybrid stochastic differential equations by feedback control based on discrete‐time observations of state and mode

Stabilisation of hybrid stochastic differential equations by feedback control based on discrete‐time observations of state and mode

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

tochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems

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