Stochastic stability and stabilization of positive systems with Markovian jump parameters

Zhang, J.; Han, Zhengzhi; Zhu, Fuliang

doi:10.1016/j.nahs.2013.12.002

Cited by 107 publications

(69 citation statements)

References 25 publications

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“…Lemma 2 [23] Matrix A is a Metzler matrix if and only if there exists a positive constant ε such that A + ε I 0.…”

Section: Lemma 1 [6] System (1) Is Said To Be Positive If and Only Ifmentioning

confidence: 99%

“…Markovian jump systems, being a special class of hybrid system, can model many practical control processes and systems subject to abrupt changes in their structures, such as networked control systems [20], manufacturing systems [18], fault-detection systems [8], and system theory [1,12,14,16,17]. In some cases, positive systems subject to some random changes are modeled as positive Markovian jump systems; recent papers have reported on their stability [2,23], stabilization [23], and filter design [25].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, though, theoretical predictions from linear co-positive Lyapunov functions have been published in [2,4,5,9,15,[21][22][23][24][25], which differ from those of the former. The nonnegative property of positive systems makes linear Lyapunov functions suitable candidates.…”

Section: Introductionmentioning

confidence: 99%

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Finite-Time $$L_1$$ L 1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates

Wang

Gao

2015

Circuits Syst Signal Process

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The paper deals with the problem of finite-time L 1 control for positive Markovian jump systems with partly known transition rates. Firstly, by constructing a linear co-positive Lyapunov function, sufficient conditions for finite-time boundedness and L 1 finite-time boundedness of the open-loop system are developed. Then, an effective method is proposed for the construction of the state feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, two examples are given, which include a mathematical model of virus mutation treatment to illustrate the validity of the obtained results.

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“…Lemma 2 [23] Matrix A is a Metzler matrix if and only if there exists a positive constant ε such that A + ε I 0.…”

Section: Lemma 1 [6] System (1) Is Said To Be Positive If and Only Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite-Time $$L_1$$ L 1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates

Wang

Gao

2015

Circuits Syst Signal Process

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“…Examples include networked control systems [36], manufacturing systems [11], faultdetection systems [16], and system control theory [25,27]. Recently, there are some results about positive Markovian jump systems include stability [4,28,46], stabilization [35,46], filter design [50], and time delay [34]. To mention a few, researchers proposed sufficient conditions for stochastic stability of the underlying systems were proposed and designed the state feedback controller such that the closed-loop systems were positive and stochastically stable in [46].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, there are some results about positive Markovian jump systems include stability [4,28,46], stabilization [35,46], filter design [50], and time delay [34]. To mention a few, researchers proposed sufficient conditions for stochastic stability of the underlying systems were proposed and designed the state feedback controller such that the closed-loop systems were positive and stochastically stable in [46]. The problem of L 1 control for positive Markovian jump systems with time-varying delays and partly known transition rates was addressed in [34].…”

Section: Introductionmentioning

confidence: 99%

Stabilization for Positive Markovian Jump Systems with Actuator Saturation

Gao

Kao

et al. 2016

Circuits Syst Signal Process

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This paper considers stabilization for positive Markovian jump systems in the presence of actuator saturation. Firstly, we use a Lyapunov function approach and convex analysis to derive sufficient conditions for stochastic stability and positivity of the continuous-and discrete-time cases. Then, the state feedback controller design and the estimate of the domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities. Finally, numerical examples are given to demonstrate the validity of the main results.

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Adaptive event‐triggered fault detection for nonlinear positive semi‐Markov jump systems

Zhang

Lin

2022

Adaptive Control & Signal

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Summary This article investigates the asynchronous fault detection filter of nonlinear positive semi‐Markov jump systems with disturbances and actuator faults based on adaptive event‐triggering scheme. First, an adaptive event‐triggering strategy in the linear form is presented and a framework on the fault detection filter is established. Then, a hidden semi‐Markov model is introduced to describe the asynchronous phenomenon between the original system and the filter and thus an augmented fault detection system is constructed. Using stochastic Lyapunov functions and linear programming, the filter gains are determined for guaranteeing the positivity and stochastic stability with hybrid L1$$ {L}_1 $$ performance. Compared with existing results, the novelties of the proposed design lie in: (i) a new adaptive event‐triggered strategy is constructed, which improves the existing static one, (ii) an adaptive event‐triggered asynchronous filter is proposed for the underlying systems, (iii) hybrid gain performances of the filter are obtained with respect to the disturbance and fault, and (iv) a linear programming‐based computation method is given to determine the filter gains. Finally, one illustrate example is provided to verify the validity of the results in this article.

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Stochastic stability and stabilization of positive systems with Markovian jump parameters

Cited by 107 publications

References 25 publications

Finite-Time $$L_1$$ L 1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates

Finite-Time $$L_1$$ L 1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates

Stabilization for Positive Markovian Jump Systems with Actuator Saturation

Adaptive event‐triggered fault detection for nonlinear positive semi‐Markov jump systems

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