Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates

Jiang, Baoping; Gao, Cunchen; Kao, Yonggui; Liu, Zhen

doi:10.1016/j.amc.2016.05.038

Cited by 22 publications

(13 citation statements)

References 29 publications

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“…Some sufficient existence conditions are presented in Theorems and respectively. Compared with existing references , the proposed SMC law here depends on TRM by using

ℒ S false(t false)

, it could reflect the effect of Markovian jumping directly and the control effect is better.…”

Section: Resultsmentioning

confidence: 99%

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Wang

Tong

2018

Asian Journal of Control

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In this paper, the sliding mode control (SMC) problem for continuous-time Markovian jump systems (MJSs) is considered, in which the transition rate matrix (TRM) is partially unknown and uncertain. Firstly, the sliding mode surface S(t) = 0 is designed, which is mode-dependent. Therefore, ℒ S(t) is used instead ofṠ(t) in the SMC algorithm. Via adopting a linear matrix inequality (LMI) approach, sufficient conditions are proposed to ensure that the reduced order system is exponentially stable in mean square. Furthermore, the reduced order system is completely insensitive to the external disturbance. Secondly, SMC law is designed correspondingly which dominated by a Markov process. It could drive the state trajectories onto the specified sliding mode surface in finite time quickly and maintain them on the surface in subsequently time. Thirdly, a new term in ℒ S(t) will be introduced in the designed SMC and should be handled by a new approach. Finally, a numerical example is provided to show the effectiveness of the proposed method.

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“…Some sufficient existence conditions are presented in Theorems and respectively. Compared with existing references , the proposed SMC law here depends on TRM by using

ℒ S false(t false)

, it could reflect the effect of Markovian jumping directly and the control effect is better.…”

Section: Resultsmentioning

confidence: 99%

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Wang

Tong

2018

Asian Journal of Control

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“…Step 3: Obtain a pair of RCF {N (t, s), D(t, s)}. From RCF (16), a pair of particular solutions can be given by…”

Section: General Proceduresmentioning

confidence: 99%

“…The phenomenon of time-delay exists widely in fields such as mechanical transmission [16], network control systems [17], communication [18], and chemical engineering [19]. The rate of state change for time-delay systems depends on the past state, which is an essential cause of the instability of systems.…”

Section: Introductionmentioning

confidence: 99%

Linear Function Observers for Linear Time-Varying Systems With Time-Delay: A Parametric Approach

Liu

Yang³

2020

IEEE Access

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In this paper, a parametric approach to design a Luenberger functional observer for linear time-varying (LTV) systems with time-delay is investigated. Based on the solution to generalized Sylvester equation (GSE), the complete general parametric expressions for the functional observer gain matrices are established with the time-varying coefficient matrices, the time-varying closed-loop system and a group of arbitrary parameters. With the parametric method, the observation error system can be transformed into a linear system with the expected eigenstructure. Finally, a numerical simulation is provided to illustrate the effectiveness of the parametric approach. INDEX TERMS Functional observers, LTV systems with time-delay, parametric method, Sylvester equation.

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“…e Markovian jump system (MJS) refers to a stochastic system with multiple model states and the system transitions between modes in accordance with the properties of the Markov chain due to the multimode transition characteristics of the Markovian jump system in the actual engineering. It can be used to simulate many systems with abrupt characteristics, such as manufacturing systems and faulttolerant systems [14][15][16][17][18][19][20][21][22][23][24]. In [25], the exponential L 2 -L ∞ filter problem of the linear system is explored, and the system has both distributed delay, Markovian jump parameter, and norm bounded parameter uncertainty.…”

Section: Introductionmentioning

confidence: 99%

H_∞ Filter Design for Networked Control Systems: A Markovian Jump System Approach

Wang

Sun

2020

Discrete Dynamics in Nature and Society

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is paper puts forward a method to design the H ∞ filter for networked control systems (NCSs) with time delay and data packet loss. Based on the properties of Markovian jump system, the packet loss is treated as a constant probability independent and identically distributed Bernoulli random process. us, the stochastic stability condition can be acquired for the filtering error system, which meets an H ∞ performance index level c. It is shown that, by introducing a special structure of the relaxation matrix, a linear representation of the filter meeting an H ∞ performance index level for NCSs with time delay and packet loss can be obtained, which uses linear matrix inequalities (LMIs). Finally, numerical simulation examples demonstrate the effectiveness of the proposed method.Hindawi

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Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates

Cited by 22 publications

References 29 publications

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Linear Function Observers for Linear Time-Varying Systems With Time-Delay: A Parametric Approach

H_∞ Filter Design for Networked Control Systems: A Markovian Jump System Approach

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Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates

Cited by 22 publications

References 29 publications

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Linear Function Observers for Linear Time-Varying Systems With Time-Delay: A Parametric Approach

H∞ Filter Design for Networked Control Systems: A Markovian Jump System Approach

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H_∞ Filter Design for Networked Control Systems: A Markovian Jump System Approach