Robust integral sliding mode control for Markovian jump systems: A singular system approach

Zohrabi, Nasibeh; Abolmasoumi, Amir Hossein; Momeni, Hamid Reza; Abdelwahed, Sherif

doi:10.1109/acc.2016.7526811

Cited by 4 publications

(7 citation statements)

References 29 publications

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“…whereM(i) = X (i)M(i)X (i). Applying Schur complement formula for inequalities (19), (20) and (21), such that (19) is equivalent to (8), (20) is equivalent to (9) and (21) is equivalent to (10). That is, the constructed Lyapunov function ℒ V (t) < 0.…”

Section: Resultsmentioning

confidence: 99%

“…A class of variable structure system is the so-called Markovian jump systems (MJSs) on account of the abrupt change dominated by a Markov process [4][5][6]. In an MJS, the dynamical system is described by a set of structures, and the structure switching is controlled by a Markov process in a finite space [7][8][9][10][11]. During the past decades, some stochastic switching phenomenon can be described by MJSs effectively, such as air vehicles [12], power systems [13,14], economic systems [13,15,16], and engineering technology [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…Yanhui Wang is the corresponding author (e-mail: wangyanhui@lnpu.edu.cn). This work was supported by the National Natural Science Foundation of China under Grants 61374043 and 61473140, the Program for Liaoning Excellent Talents in University under Grant LJQ2013040, the Natural Science Foundation of Liaoning Province under Grant 2014020106. structure system and has received a great deal of attention [10,29,30]. It could reduce the complex high-order system into two independent low-order systems.…”

Section: Introductionmentioning

confidence: 99%

“…In another area of research, sliding mode control (SMC) is an effective method for dealing with variable structure system and has received a great deal of attention . It could reduce the complex high‐order system into two independent low‐order systems.…”

Section: Introductionmentioning

confidence: 99%

“…The SMC law could drive the state trajectories of the closed‐loop system from arbitrary initial values onto the designed sliding mode surface quickly in finite time and retain the sliding motion in the sequent time. This process is called reaching phase . Up to now, many research topics of SMC algorithms have been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Wang

Tong

2018

Asian Journal of Control

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An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities

Zohrabi

Zakeri

Abolmasoumi

et al. 2018

Int. J. Dynam. Control

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This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method is general enough to cover a wide spectrum of systems from those with completely known transition probability rates to those with completely unknown transition probability rates. Based on some mode-dependent Lyapunov-Krasovski functionals and making use of the freeconnection weighting matrices, new delay-dependent conditions guaranteeing the existence of linear switching surfaces and the stochastic stability of sliding mode dynamics are derived in terms of linear matrix inequalities (LMIs). Then, a sliding mode controller is designed such that the resulted closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. This paper also proposes an adaptive sliding mode controller design method which applies to cases in which modedependent time-varying delays are unknown. All the conditions obtained in this paper are in terms of LMI feasibility problems. Numerical examples are given to illustrate the effectiveness of the proposed methods.

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Sliding Mode Control of Markovian Jump System via an Event-triggered Mechanism

Wang

Yang

et al. 2019

2019 Chinese Automation Congress (CAC)

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Robust integral sliding mode control for Markovian jump systems: A singular system approach

Cited by 4 publications

References 29 publications

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities

Sliding Mode Control of Markovian Jump System via an Event-triggered Mechanism

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