A delay decomposition approach to fuzzy Markovian jumping genetic regulatory networks with time-varying delays

Balasubramaniam, P.; Sathy, R.; Rakkiyappan, R.

doi:10.1016/j.fss.2010.10.010

Cited by 22 publications

(10 citation statements)

References 34 publications

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“…For GRN (2) with a delay satisfying (5), the following stability criterion is derived by using the proposed WTDII (27), together with Lemmas 1, 2, and 5, to estimate the derivative of the LKF. …”

Section: Stability Of Grn (2) With Delay Satisfying (5)mentioning

confidence: 99%

“…For some cases, the change rates of the time-varying delays are unmeasurable, that is, time delay satisfying (6). For this case, the following stability criterion can be derived by using the proposed WTDII (27), together with Lemmas 1, 2, 5, and 8, to estimate the derivative of the LKF. …”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…However, local stability is not enough for understanding nonlinear GRNs; the globally asymptotical stability of GRNs with SUM regulatory functions has been widely investigated [17][18][19][20][21][22]. Meanwhile, by taking into account the unavoidable uncertainties caused by modelling errors and parameter fluctuations, many scholars paid attentions to the robust stability analysis of the delayed GRNs [23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Moreover, both the intrinsic noise derived from the random births and deaths of individual molecules and the extrinsic noise due to environment fluctuations make the gene regulation process 2 Mathematical Problems in Engineering an intrinsically noisy process [59].…”

Section: Introductionmentioning

confidence: 99%

“…The first one is the delay-partition-based LKFs, which is constructed by dividing the delay interval into several small subintervals and then replacing the original integral terms with multiple new integral terms based on delay subintervals. This type of LKF has been used to investigate the robust stability of various GRNs [25,26,51], the exponential stability of switch GRNs [56], and the stochastic stability of jumping GRNs [27,43,45]. The other is the augmented LKF constructed by using various state vectors (current and delayed and/or integrated state vectors, etc.)…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Zhu

et al. 2017

Mathematical Problems in Engineering

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Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of LyapunovKrasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range-and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature.

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Section: Stability Of Grn (2) With Delay Satisfying (5)mentioning

confidence: 99%

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Zhu

et al. 2017

Mathematical Problems in Engineering

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“…In practical applications, to research the nonlinear timedelay system, the scholars considered the T-S fuzzy timedelay model which is a kind of effective representation, and many analysis and synthesis methods for T-S fuzzy time-delay systems have been developed over the past years [8][9][10][11][12][13][14][15][16][17]. So, many scholars extended this model to Markov jump systems with time delays [18][19][20][21][22][23][24][25][26][27][28]. Reference [18] was concerned with an ∞ control for a class of T-S fuzzy Markov jump system under unreliable communication links.…”

Section: Introductionmentioning

confidence: 99%

H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

Gong

Zeng

2014

Mathematical Problems in Engineering

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This paper investigates theH∞filtering problem of discrete singular Markov jump systems (SMJSs) with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition onH∞-disturbance attenuation is presented, in which both stability and prescribedH∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependentH∞filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.

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Adaptive event‐triggered robust H_∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time‐varying delay

Aslam

Qaisar

Majid

et al. 2022

Asian Journal of Control

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This paper considers an adaptive event‐triggered robust H∞ control for the Takagi–Sugeno (T‐S) fuzzy under the networked Markov jump systems (NMJSs) with time‐varying delay. First, a new adaptive event‐triggered scheme is developed to guarantee the T‐S fuzzy NMJSs, and as a result, communication energy consumption reduced while device efficiency is maintained. Besides, an asynchronous operation method is adopted to deal with the mismatched premise variables between the fuzzy system and the fuzzy controller. One of the main objectives of this article is to construct the fuzzy state‐feedback controller (mode‐dependent) in a closed‐loop form for stochastic stability for all admissible parameter uncertainties with an H∞ performance index. Different from the conventional triggering mechanism, in this paper, the parameters of the triggering function are based on a new adaptive law that is obtained online rather than a predefined constant. To achieve the less conservative control design, a new type of stochastic Lyapunov–Krasovskii functional is designed by decomposing method, in which the delay interval transforms into various equidistant subintervals in terms of linear matrix inequalities. An example of a truck‐trailer application is used to demonstrate the effectively of the proposed algorithms.

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A delay decomposition approach to fuzzy Markovian jumping genetic regulatory networks with time-varying delays

Cited by 22 publications

References 34 publications

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

Adaptive event‐triggered robust H_∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time‐varying delay

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A delay decomposition approach to fuzzy Markovian jumping genetic regulatory networks with time-varying delays

Cited by 22 publications

References 34 publications

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

Adaptive event‐triggered robust H∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time‐varying delay

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Adaptive event‐triggered robust H_∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time‐varying delay