Recent progress in impulsive control systems

Xiao, Yang; Peng, Dongxue; Lv, Xiaoxiao; Li, Xiaodi

doi:10.1016/j.matcom.2018.05.003

Cited by 79 publications

(32 citation statements)

References 96 publications

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“…are, respectively, the states of the ith unit from the first neural field and the jth unit from the second neural field before and after an impulsive perturbation at the moment t. Note that the abrupt changes P ik (x i (t)) = ∆x i (t) = x i (t + ) − x i (t) and Q jk (y j (t)) = ∆y j (t) = y j (t + ) − y j (t) can be considered as impulsive controls [31][32][33][34][35][36][37][38].…”

Section: Preliminary Notesmentioning

confidence: 99%

“…are called impulsive moments at which impulsive control techniques can be applied [34][35][36][37][38]. Note that, in general, the number k of the hypersurface θ k may not be equal to the number l k of the impulsive moment t l k .…”

Section: Preliminary Notesmentioning

confidence: 99%

“…Since impulsive phenomena exist in numerous fields of science and engineering [25][26][27][28][29] and the impulsive control methods are find to be more efficient than other control strategies [30][31][32][33][34][35][36][37][38], there has been an increasing research interest on the impulsive generalizations of Cohen-Grossberg-type BAM neural networks with delays. For example, in [39] the problem of existence of equilibrium states of Cohen-Grossberg BAM neural networks with delays and impulses and their global exponential stability behavior are investigated using topological degree theory, the Lyapunov functional method and some analysis techniques.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

et al. 2020

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The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria.

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Section: Preliminary Notesmentioning

confidence: 99%

Section: Preliminary Notesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

et al. 2020

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“…We denote by u(t, x) = u(t, x; ϕ 0 ) the solution of the Initial Boundary Problem (IBP) (2), (3), (4). Note that, according to the theory of impulsive neural networks [20][21][22][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], the solutions (2), (3), (4) are piecewise continuous functions that have jump discontinuities at the moments t k , k = 1, 2, . .…”

Section: Preliminariesmentioning

confidence: 99%

“…See, for example, [30][31][32][33][34][35] and the references therein. In addition, the impulsive control is found to be very efficient control approach in numerous applied problems [36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

et al. 2019

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The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.

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On the almost periodicity in discontinuous impulsive gene regulatory networks

Stamov

Stamova

2021

Math Methods in App Sciences

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In this paper, the almost periodic solutions for discontinuous impulsive gene regulatory networks (GRNs) are investigated. Firstly, the concept of almost periodicity is introduced for the impulsive model under consideration. Secondly, sufficient conditions are presented for the existence, uniqueness, and global exponential stability of almost periodic solutions. To this end, an estimate of the Cauchy matrix of the model of GRNs is established. Finally, the obtained results as well as the control power of the impulses are demonstrated via examples. This research contributes to the development of the qualitative theory of impulsive GRNs in almost periodic environment.

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Recent progress in impulsive control systems

Cited by 79 publications

References 96 publications

On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

On the almost periodicity in discontinuous impulsive gene regulatory networks

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