Non-fragile control of positive Markovian jump systems

Yang, Haoyue; Zhang, Junfeng; Jia, Xianglei; Li, Shicheng

doi:10.1016/j.jfranklin.2019.02.008

Cited by 21 publications

(23 citation statements)

References 31 publications

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“…In Theorem 2, the actuators partly fail or completely fail and the fault matrices are different for each subsystem. Therefore, the fault case in Theorem 2 is more general and practical than those ones in [26][27][28].…”

Section: V(x(t))mentioning

confidence: 99%

“…For general switched systems, there have been some results on actuator faults [22][23][24][25]. The literature [26][27][28] had considered the actuator failure problem of positive systems. It is always assumed that each subsystem of hybrid systems only contains a fault.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, these components may only lose part efficacy and be not completely ineffective. These facts show that the actuator fault assumptions in [17][18][19][20][21][22][23][24][25][26][27][28] are restrictive in practice applications. The relaxation of such assumptions motivates the present work.…”

Section: Introductionmentioning

confidence: 99%

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Reliable actuator fault control of positive switched systems with double switchings

Zhang

Raïssi

2020

Asian Journal of Control

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This paper proposes a novel double switchings reliable control for positive switched systems. Double switchings refer to the switchings of subsystems and faults. Considering the actuator faults during the system operation, a class of periodic switched actuator faults is first considered. A reliable controller is designed using linear copositive Lyapunov functions and an average dwell time switching rule is presented for the systems. Then, two average dwell time switching rules are given for the subsystems and the faults, respectively. A corresponding reliable controller is proposed in terms of linear programming.Compared with existing results, the novel approach contains three advantages: (i) the actuator faults of subsystems are allowed to be varying, (ii) two classes of detailed double switchings rules are designed, and (iii) the presented reliable control framework provides a new methodology to deal with the reliable control problem of general switched systems with faults. Finally, two examples are given to illustrate the validity of the presented results.

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Section: V(x(t))mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reliable actuator fault control of positive switched systems with double switchings

Zhang

Raïssi

2020

Asian Journal of Control

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“…Few efforts are devoted to nonlinear positive systems [17] though there have been many results on general nonlinear systems (non-positive) [35], [36]. It should also be pointed out that the fault may lead to the fragile property of the actuator [32], [37]- [39]. In future work, it is interesting to develop the double switchings control framework for the non-fragile control of nonlinear positive hybrid systems.…”

Section: Choosing a Linear Co-positive Lyapunov Function Candidatementioning

confidence: 99%

“…In [31], multiple linear copositive Lyapunov functions were employed for designing the non-fragile reliable controller of positive switched systems with actuator faults. A linear programming approach was used for the non-fragile control of positive Markovian jump systems in [32]. In [33], an active fault tolerant controller of switched positive linear systems was proposed in terms of quadratic Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

Double Switchings Reliable Control of Positive Switched Systems With Unfixed Actuator Faults

Ding

Liu

et al. 2020

IEEE Access

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This paper investigates the double switchings reliable control of positive switched systems with actuator faults. Different from existing fixed actuator faults, a class of unfixed actuator faults is introduced, where each subsystem can have several faults rather than only a fault. First, a periodic occurring fault is considered for the subsystems. Using linear Lyapunov functions with linear programming, a set of reliable controllers is designed for positive switched systems. Then, an average dwell time based switching law between the normal and faulty modes of subsystems is established. In detail, the considered systems consist of several switched subsystems, where the subsystems have normal and faulty modes. In such a case, two classes of multiple linear Lyapunov functions are constructed for the subsystems and the whole switched systems, respectively. Accordingly, two classes of reliable controllers are designed for the normal and faulty modes, respectively. Meanwhile, two classes of average dwell time switching laws, named double switchings laws, are designed for the subsystems and the whole switched systems, respectively. Finally, two examples are provided to illustrate the effectiveness of the proposed design. INDEX TERMS Double switchings, positive switched systems, unfixed actuator faults.

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Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

Liu

Song

et al. 2022

Asian Journal of Control

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This paper investigates the non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults. First, a novel fault model consisting of linear and nonlinear terms is established for the systems. By constructing a stochastic co‐positive Lyapunov function, the non‐fragile reliable controller is designed for the systems with additive gain perturbations using matrix decomposition technique. Then, the proposed design is extended for dealing with multiplicative gain perturbations and variable gain perturbations. Under the designed controllers, the resulting closed‐loop systems are positive and stochastically stable. All presented conditions are solvable in terms of linear programming. Finally, two illustrative examples are provided to verify the effectiveness of the theoretical results.

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Non-fragile control of positive Markovian jump systems

Cited by 21 publications

References 31 publications

Reliable actuator fault control of positive switched systems with double switchings

Reliable actuator fault control of positive switched systems with double switchings

Double Switchings Reliable Control of Positive Switched Systems With Unfixed Actuator Faults

Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

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