Stabilization computation for a kind of uncertain switched systems using non-fragile sliding mode observer method

A non-fragile sliding mode control problem will be investigated in this article. The problem focuses on a kind of uncertain switched singular time-delay systems in which the state is not available. First, according to the designed non-fragile observer, we will construct an integral-type sliding surface, in which the estimated unmeasured state is used. Second, we synthesize a sliding mode controller. The reachability of the specified sliding surface could be proved by this sliding mode controller in a finite time. Moreover, linear matrix inequality conditions will be developed to check the exponential admissibility of the sliding mode dynamics. After that, the gain matrices designed will be given along with it. Finally, some numerical result will be provided, and the result can be used to prove the effectiveness of the method.

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Observer-Based $$H_\infty $$ H ∞ Sliding Mode Controller Design for Uncertain Stochastic Singular Time-Delay Systems

Circuits Systems and Signal Processing ◽

10.1007/s00034-015-0049-x ◽

2015 ◽

Vol 35 (1) ◽

pp. 63-77 ◽

Cited By ~ 21

Author(s):

Yonggui Kao ◽

Jing Xie ◽

Changhong Wang ◽

Hamid Reza Karimi

Keyword(s):

Time Delay ◽

Controller Design ◽

Sliding Mode ◽

Delay Systems ◽

Sliding Mode Controller ◽

Time Delay Systems ◽

Singular Time

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Applying Output Feedback Integral Sliding Mode Controller to Time-Delay Systems

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e94.a.1051 ◽

2011 ◽

Vol E94-A (4) ◽

pp. 1051-1058 ◽

Cited By ~ 1

Author(s):

Huan-Chan TING ◽

Jeang-Lin CHANG ◽

Yon-Ping CHEN

Keyword(s):

Time Delay ◽

Output Feedback ◽

Sliding Mode ◽

Delay Systems ◽

Sliding Mode Controller ◽

Time Delay Systems ◽

Integral Sliding Mode

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Linear Quadratic Nash Game of Stochastic Singular Time-Delay Systems with Multiple Decision Makers

Journal of Systems Science and Information ◽

10.1515/jssi-2015-0472 ◽

2015 ◽

Vol 3 (5) ◽

pp. 472-480

Author(s):

Huainian Zhu ◽

Guangyu Zhang ◽

Chengke Zhang ◽

Ying Zhu ◽

Haiying Zhou

Keyword(s):

Time Delay ◽

Decision Makers ◽

Delay Systems ◽

Linear Matrix ◽

Time Delay Systems ◽

Linear Quadratic ◽

Nash Game ◽

Multiple Decision Makers ◽

Nash Strategies ◽

Singular Time

AbstractThis paper discusses linear quadratic Nash game of stochastic singular time-delay systems governed by Itô’s differential equation. Sufficient condition for the existence of Nash strategies is given by means of linear matrix inequality for the first time. Moreover, in order to demonstrate the usefulness of the proposed theory, stochastic H2∕H∞control with multiple decision makers is discussed as an immediate application.

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Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

Journal of Vibration and Control ◽

10.1177/1077546321989202 ◽

2021 ◽

pp. 107754632198920

Author(s):

Zeinab Fallah ◽

Mahdi Baradarannia ◽

Hamed Kharrati ◽

Farzad Hashemzadeh

Keyword(s):

Transition Probabilities ◽

Sliding Mode ◽

Transition Probability ◽

Transition Probability Matrix ◽

Linear Matrix ◽

Sliding Mode Controller ◽

Sliding Surface ◽

Markovian Jump ◽

Markovian Jump System ◽

Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

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Sliding Mode H∞-Control with Stochastic Time Delay Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.321-324.1712 ◽

2013 ◽

Vol 321-324 ◽

pp. 1712-1718

Author(s):

Ravi Kumar ◽

Kil To Chong

Keyword(s):

Time Delay ◽

Sliding Mode ◽

Estimation Error ◽

Sufficient Conditions ◽

Feedback Stabilization ◽

Delay Systems ◽

Linear Matrix ◽

Linear Filter ◽

Time Delay Systems ◽

Stochastic Time

In this paper, we concerned the problem of sliding mode of-control with stochastic stabilization of uncertainty. Some sufficient conditions are derived for this class of robust feedback stabilization of time delay systems. The stochastic time delay systems may switch from one to one corresponds of linear filter, such that the dynamics of estimation error is guaranteed to be stochastically stable in mean square. Moreover, it is shown that for a class of special linear stochastic neutral systems, the H-sliding mode control design can be obtained by solving linear matrix inequalities (LMIs).

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