Stabilization of Switched Stochastic Genetic Regulatory Networks with Leakage and Impulsive Effects

Pandiselvi, S.; Raja, R.; Cao, Jinde; Rajchakit, Grienggrai

doi:10.1007/s11063-018-9843-3

Cited by 25 publications

(7 citation statements)

References 22 publications

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“…Similarly, we can define the changes of V (y ς ) at impulse times ς = ς k , k ∈ Z + . By (15) we have Therefore the stochastic genetic regulatory network ( 9) is passive under Definition 1, which completes the proof.…”

Section: Discussionmentioning

confidence: 59%

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Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

Senthilraj¹,

Saravanakumar

Raja

et al. 2021

Adv Differ Equ

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This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.

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Section: Discussionmentioning

confidence: 59%

“…Recently, Zhang et al [14] reported the problem of stochastic GRNs subject to mixed time-varying delays in mean square asymptotically stable condition. Under the Lyapunov stability and new integral techniques, a new set of sufficient conditions is derived in [15] for the stability of GRNs with stochastic perturbations.…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

Senthilraj¹,

Saravanakumar

Raja

et al. 2021

Adv Differ Equ

Self Cite

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“…Nonlinear systems, being a kind of thoroughly common system encountered in practical engineering applications, have owned more excellent results in these years. The aforementioned outstanding results range from inverted pendulum [1], DC microgrids [2] to genetic regulatory networks (GRNs) [3]. Nevertheless, for the two former great achievements, all the ultimately investigated systems have been changed to the combination of linear systems by the T-S fuzzy logic systems.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Tracking Control for Persistent Dwell-Time Switched Nonlinear Systems With Uncertainty

et al. 2019

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In this note, the tracking control issue for the switched nonlinear systems with equationdependent uncertainty is investigated. The relatively general switching law, persistent dwell-time, is employed to describe the switching property appearing in the uncertainty. The employ of the equationdependent uncertainty makes the design with higher accuracy when the uncertainties are extremely different from each other. Subsequently, combining with the law of switching times for the persistent dwell-time and the new requirement on the Lyapunov function at the switching instant, the global uniform boundedness of the error variable is obtained. Finally, the feasibility of the design scheme proposed is testified via a numerical example. INDEX TERMS Switched nonlinear systems, uncertainty, persistent dwell-time, global uniform boundedness.

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“…In [8], some synchronization conditions for an impulsive and switching dynamical network were developed by applying an average impulsive dwell-time method. Notably, some researchers have focused on the dynamic behavior for a time-delay GRN with impulsive effects or switching mechanisms because of the abrupt change of model parameters and system state [20,29,9,6,19,10]. In particular, by employing a new LKF and the PDT method, some exponential stability criteria were presented for the discrete time-delay switched GRNs in [29].…”

mentioning

confidence: 99%

“…With the aid of the Metzler and nonnegative matrices, the equivalent state bounding criteria are further established when the impulses in ISGRNs vanish. In comparison with some existing literatures [20,19,10], the adopted method avoids the construct of LKF or auxiliary function, and hence reduces the computational complexity.…”

mentioning

confidence: 99%

State bounding for time-delay impulsive and switching genetic regulatory networks with exogenous disturbance

Yan¹,

Zhang²,

Hu³

et al. 2022

DCDS-S

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<p style='text-indent:20px;'>This paper focuses on the state bounding problem for the time-delay impulsive and switching genetic regulatory networks (ISGRNs) with exogenous disturbances. Firstly, a sufficient criterion for the state bounding is obtained such that all the trajectories of ISGRNs under consideration converge exponentially into a sphere on the basis of an average dwell time (ADT) switching. Besides, globally exponential stability conditions for the considered system are further stated when the exogenous disturbance vanishes. As a special case, the equivalent state bounding criteria are established by using the properties of some special matrices when there exist no impulses at the switching instants in ISGRNs. Finally, an illustrating example is given to demonstrate the derived results. Compared with the existing literatures, the considered genetic regulatory networks (GRNs) have more general structure and the approach adopted in the present paper is more simple than Lyapunov-Krasovskii functional (LKF) approach.</p>

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Stabilization of Switched Stochastic Genetic Regulatory Networks with Leakage and Impulsive Effects

Cited by 25 publications

References 22 publications

Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

Adaptive Tracking Control for Persistent Dwell-Time Switched Nonlinear Systems With Uncertainty

State bounding for time-delay impulsive and switching genetic regulatory networks with exogenous disturbance

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