New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

Zhao, Yanfeng; Shen, Jihong; Chen, Dongyan

doi:10.1155/2016/7634680

Cited by 3 publications

(2 citation statements)

References 45 publications

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“…For example, the robust ∞ control problem has been investigated in [16] for discrete delayed stochastic GRNs. Moreover, the asymptotic stability problems have been investigated in [17][18][19] for discrete-time uncertain GRNs with time-varying delays and stochastic fluctuations, where some sufficient conditions have been presented to ensure the stability of the addressed GRNs via the linear matrix inequality approach.…”

Section: Introductionmentioning

confidence: 99%

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

2017

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We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks (GRNs) with timevarying delays and randomly occurring uncertainties. In particular, the norm-bounded uncertainties enter into the GRNs in random ways in order to reflect the characteristic of the modelling errors, and the so-called randomly occurring uncertainties are characterized by certain mutually independent random variables obeying the Bernoulli distribution. The focus of the paper is on developing a new nonfragile state estimation method to estimate the concentrations of the mRNA and the protein for considered uncertain delayed GRNs, where the randomly occurring estimator gain perturbations are allowed. By constructing a LyapunovKrasovskii functional, a delay-dependent criterion is obtained in terms of linear matrix inequalities (LMIs) by properly using the discrete-time Wirtinger-based inequality and reciprocally convex combination approach as well as the free-weighting matrix method. It is shown that the proposed method ensures that the estimation error dynamics is globally asymptotically stable and the desired estimator parameter is designed via the solutions to certain LMIs. Finally, we provide two numerical examples to illustrate the feasibility and validity of the proposed estimation results.

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Section: Introductionmentioning

confidence: 99%

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

2017

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“…So far, many conclusions about T-S fuzzy systems have been drawn. For example, robust control of uncertain T-S fuzzy systems was studied in [18,4], control for uncertain T-S fuzzy systems and stability analysis of T-S fuzzy systems were investigated in [2,24,23,16], the robust stabilization problem for discrete time-varying system with parameter uncertainties and disturbances was concerned in [8,25]. For uncertain T-S fuzzy systems with input delays, most scholars conducted stability analysis by designing Lyapunov function and adopting linear matrix inequality (LMI) method.…”

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confidence: 99%

Sliding mode control for uncertain T-S fuzzy systems with input and state delays

Li¹,

Zhang²,

Zhang³

et al. 2020

NACO

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In this paper, the problem of sliding mode control (SMC) for uncertain T-S (Tagaki-Sugeno) fuzzy systems with input and state delays is investigated , in which the nonlinear uncertain terms are unknown,and also unmatched. For the T-S fuzzy model of the controlled object, a method based on sliding mode compensator is designed, and the system is controlled by sliding mode. Based on solving linear matrix inequalities (LMI), we obtain the design method of sliding mode and controller. The sufficient conditions for the asymptotical stability of the sliding mode dynamics are given by using LMI technique and the Lyapunov stability theory, and it has been shown that the state trajectories can be driven onto the sliding surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theories.

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State Bounding Description and Reachable Set Estimation for Discrete-Time Genetic Regulatory Networks With Time-Varying Delays and Bounded Disturbances

Xue

Liu

Zhang

2022

IEEE Trans. Syst. Man Cybern, Syst.

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New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

Cited by 3 publications

References 45 publications

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

Sliding mode control for uncertain T-S fuzzy systems with input and state delays

State Bounding Description and Reachable Set Estimation for Discrete-Time Genetic Regulatory Networks With Time-Varying Delays and Bounded Disturbances

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