Robust stabilisation for non‐linear time‐delay semi‐Markovian jump systems via sliding mode control

Qi, Wenhai; Park, Ju H.; Cheng, Jun; Kao, Yonggui

doi:10.1049/iet-cta.2016.1465

Cited by 87 publications

(41 citation statements)

References 43 publications

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“…Remark Usually, for Markovian jump systems with time‐varying delays, if we want to obtain the delay‐dependent criteria, the Lyapunov functional is chosen as

V false(x_{t}, σ_{t}, t false) = x^{T} false(t false) P_{σ false(t false)} x false(t false) + \int_{t - τ_{M}}^{t} x^{T} false(s false) Q x false(s false) d s + \int_{t - τ_{M}}^{t} \int_{θ}^{t} x^{T} false(s false) W x false(s false) d s d θ

whose parameters in integral term are mode independent, which may lead to some conservativeness. In our work, a proper mode‐dependent Lyapunov functional is constructed to get the delay‐dependent criteria, and the parameters in the single integral term of V ( x t , σ t , t ) are mode dependent, which may reduce some conservativeness regardless of the increasing computational complexity . Furthermore, augmented Lyapunov‐Krasovskii functionals or Lyapunov‐Krasovskii functionals with multiple‐integral terms may contribute to further reduce the conservativeness for the time‐delay systems, but the Lyapunov function is more complicated and will bring more tedious computations.…”

Section: Resultsmentioning

confidence: 99%

“…In our work, a proper mode-dependent Lyapunov functional (11) is constructed to get the delay-dependent criteria, and the parameters in the single integral term of V(x t , t , t) are mode dependent, which may reduce some conservativeness regardless of the increasing computational complexity. 29 Furthermore, augmented Lyapunov-Krasovskii functionals 30 or Lyapunov-Krasovskii functionals with multiple-integral terms 31 may contribute to further reduce the conservativeness for the time-delay systems, but the Lyapunov function is more complicated and will bring more tedious computations.…”

Section: H ∞ Performance Analysismentioning

confidence: 99%

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H_∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

2019

Intl J Robust & Nonlinear

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Summary This paper aims to solve the H∞ stabilization problem for networked semi‐Markovian jump systems subject to randomly occurring uncertainties by an improved event‐triggered technique. A new measurement error that is defined as the difference value between the latest transmitted data and the mean value of both current data and latest transmitted data is introduced into the event‐triggered condition. Compared with traditional dynamic event‐triggered scheme, more unexpected data could be avoided to be transmitted, which is demonstrated in the simulation through sufficient comparison experiments. Furthermore, by employing a Lyapunov‐Krasovskii functional method and a free‐weighting matrix method, sufficient conditions are derived to guarantee the stabilization of the closed‐loop semi‐Markovian jump time‐delay system with uncertainties and a prescribed performance index. Then, a codesign method for H∞ controller gains and event‐triggered parameters is presented. Finally, simulations are given to verify the effectiveness of our improved dynamic event‐triggered scheme.

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“…Remark Usually, for Markovian jump systems with time‐varying delays, if we want to obtain the delay‐dependent criteria, the Lyapunov functional is chosen as

V false(x_{t}, σ_{t}, t false) = x^{T} false(t false) P_{σ false(t false)} x false(t false) + \int_{t - τ_{M}}^{t} x^{T} false(s false) Q x false(s false) d s + \int_{t - τ_{M}}^{t} \int_{θ}^{t} x^{T} false(s false) W x false(s false) d s d θ

Section: Resultsmentioning

confidence: 99%

Section: H ∞ Performance Analysismentioning

confidence: 99%

H_∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

2019

Intl J Robust & Nonlinear

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“…Such controller is also insensitive to the external perturbation and parameter variation . A few results on SMC for switched systems and singular systems with or without time‐varying delays have been considered . However, there is not much work on SMC for singular switched systems with time‐varying delays.…”

Section: Introductionmentioning

confidence: 99%

Robust nonfragile observer‐based control of switched discrete singular systems with time‐varying delays: A sliding mode control design

Han

Kao

Park

2018

Intl J Robust & Nonlinear

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This paper is devoted to the robust ℋ ∞ sliding mode control issue for a type of switched discrete singular systems with time-varying delays under arbitrary switching. Since the system states are not available, the nonfragile observer strategy is used to generate the state estimation. By designing a novel sliding surface function, which is established on the estimation, new sufficient conditions via linear matrix inequalities are derived so that the closed-loop system is admissible with an ℋ ∞ disturbance attenuation level . Furthermore, sliding mode controllers are given to guarantee the reachability of the quasi-sliding mode and weaken the chattering. At last, examples are presented to verify the validity of our provided approach.

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“…Hence, much effort has been devoted to eliminating the negative effects of time-delays onto whole system performance and a great number of SMC techniques have been developed for delayed systems with different types of time-delays, see e.g. Qi, Park, Cheng, & Kao (2017), Jiang, Kao, & Gao (2017), Hu, Wang, Gao, & Stergioulas (2012b) and Wu, Su, & Shi (2012). To be specific, the problem of robust stabilization has been tackled in Qi et al (2017) for semi-MJSs with time-varying delays via SMC method.…”

Section: Introductionmentioning

confidence: 99%

“…Qi, Park, Cheng, & Kao (2017), Jiang, Kao, & Gao (2017), Hu, Wang, Gao, & Stergioulas (2012b) and Wu, Su, & Shi (2012). To be specific, the problem of robust stabilization has been tackled in Qi et al (2017) for semi-MJSs with time-varying delays via SMC method. In Jiang et al (2017), the integrator-based robust H ∞ SMC method has been proposed for stochastic MJSs with slow time-varying delays.…”

Section: Introductionmentioning

confidence: 99%

Robust H_∞ control for delayed systems with randomly varying nonlinearities under uncertain occurrence probability via sliding mode method

Zhang

et al. 2018

Systems Science & Control Engineering

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In this paper, we address the problem of robust H ∞ sliding mode control (SMC) for a class of discretetime stochastic systems with parameter uncertainties, time-varying delay and randomly varying nonlinearities (RVNs) under uncertain occurrence probability. Here, the norm-bounded parameter uncertainties are considered. The time-varying delay is bounded with known upper and lower bounds. In addition, the RVNs are depicted by using a Bernoulli distributed stochastic variable with uncertain occurrence probability. The aim of the paper is to provide an SMC method such that, for all parameter uncertainties, time-varying delay and RVNs, the robust asymptotic stability with a prescribed disturbance attenuation level is guaranteed for the sliding mode dynamics by providing a new sufficient condition. Moreover, the reachability analysis is carried out simultaneously, i.e. the states of the closed-loop system are driven onto a neighborhood of pre-designed sliding surface by synthesizing a robust sliding mode controller. Finally, the usefulness of the aforementioned control technique is verified by a numerical example. ARTICLE HISTORY

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Robust stabilisation for non‐linear time‐delay semi‐Markovian jump systems via sliding mode control

Cited by 87 publications

References 43 publications

H_∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

H_∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

Robust nonfragile observer‐based control of switched discrete singular systems with time‐varying delays: A sliding mode control design

Robust H_∞ control for delayed systems with randomly varying nonlinearities under uncertain occurrence probability via sliding mode method

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Robust stabilisation for non‐linear time‐delay semi‐Markovian jump systems via sliding mode control

Cited by 87 publications

References 43 publications

H∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

H∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

Robust nonfragile observer‐based control of switched discrete singular systems with time‐varying delays: A sliding mode control design

Robust H∞ control for delayed systems with randomly varying nonlinearities under uncertain occurrence probability via sliding mode method

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H_∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

H_∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

Robust H_∞ control for delayed systems with randomly varying nonlinearities under uncertain occurrence probability via sliding mode method