Dissipativity and exponential state estimation for quaternion-valued memristive neural networks

Li, Ruoxia; Gao, Xingbao; Cao, Jinde; Zhang, Kai

doi:10.1016/j.neucom.2019.07.036

Cited by 20 publications

(8 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lipschitz function, that is, for a non-negative constant λ ε , the following condition is satisfied: Remark 2 At present, there are too many results on QVNNs to enumerate, and the Introduction has mentioned some of them, such as [15][16][17][18][19][20][21][22][23][24]. In these papers, various time delays, memristors, parameter uncertainties, leakage, and so on are considered in the basic QVNNs, but no paper has considered the spatial factors in QVNNs so far.…”

Section: Construction Of the Considered Innsmentioning

confidence: 99%

“…For the stability analysis of QVNNs, [15] considered both discrete and distributed delays in QVNNs; [16] employed the decomposition and direct approaches, and established global μ-stability and exponential stability criteria, respectively; and [17] analyzed the multistability of QVNNs. For the dissipativity analysis of QVNNs, [18] analyzed global dissipativity of delayed QVNNs; [19] studied dissipativity issue for memristor-based QVNNs; and global dissipativity of quaternion-valued BAM NNs was analyzed in [20]. Additionally, for the synchronization of QVNNs, [21] studied the global Mittag-Leffler synchronization issue of fractional-order QVNNs; [22] obtained synchronization criterion for QVNNs with considering leakage and discrete delays; and to improve the control precision and efficiency, the finite-time synchronization and fixed-time synchronization of QVNNs were researched in [23,24], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…(i) In existing papers related to QVNNs, such as [15][16][17][18][19][20], the influence of spatial factors was ignored. Considering that the diffusion phenomenon is inevitable in real QVNNs, this paper involves reaction-diffusion terms when modeling QVNNs, which means that the system model considered in this paper may be more general and practical than previous QVNNs models.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synchronization in Fixed Time for Reaction–Diffusion Quaternion-Valued NNs with Nonlinear Interconnected Protocol and Its Application

Man

Song

2021

Neural Process Lett

View full text Add to dashboard Cite

This paper makes an interesting attempt to interconnect N quaternion-valued neural networks (QVNNs) with reaction-diffusion items by a nonlinear coupling protocol, which generates a meaningful issue of synchronization for the N subsystems. By designing a novel nonlinear feedback controller, the N subsystems can be synchronized in a fixed time, which is more efficient and practical than asymptotic synchronization. Based on the Lyapunov functional theory and fixed-time stability criterion, and by employing suitable inequality techniques, the fixed-time synchronization theorem of the nonlinear interconnected QVNNs with reactiondiffusion terms can be obtained. Furthermore, an application example that applies the main results to secure communication is provided, and the effectiveness and superiority of the proposed cryptosystem can be illustrated through comparisons.

show abstract

Section: Construction Of the Considered Innsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Synchronization in Fixed Time for Reaction–Diffusion Quaternion-Valued NNs with Nonlinear Interconnected Protocol and Its Application

Man

Song

2021

Neural Process Lett

View full text Add to dashboard Cite

show abstract

“…Very recently, quaternion‐valued neural networks have been demonstrated better performances in image compression, 3D wind forecasting, color night vision, and so on. Owing to the wide applications of quaternion‐valued neural networks, its theoretical analysis has received increasing attention . In Song and Chen , the multistability analysis of quaternion‐valued neural networks have been considered by constructing a proper auxiliary function.…”

Section: Introductionmentioning

confidence: 99%

“…Owing to the wide applications of quaternion-valued neural networks, its theoretical analysis has received increasing attention. [28][29][30][31][32][33] In Song and Chen 29, the multistability analysis of quaternion-valued neural networks have been considered by constructing a proper auxiliary function. In Chen et al 33, the stability conditions were derived based on a discrete-time quaternion-valued system.…”

mentioning

confidence: 99%

Exponential synchronization and state estimation of inertial quaternion‐valued Cohen‐Grossberg neural networks: Lexicographical order method

Wei

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary This paper addresses the problems of synchronization and state estimation for a class of inertial quaternion‐valued Cohen‐Grossberg neural networks. By means of proper control strategy, sufficient conditions are derived for ascertaining exponential synchronization of quaternion‐valued Cohen‐Grossberg neural networks. Subsequently, the state estimation problem has also been augmented to achieve robust stable performance of the estimation error system. What should be mentioned is that, the system states considered in this paper are taking values in an interval, which implies that the states are varying between two different quaternions, thus, an optimal algorithm (lexicographical order method) is employed, which can be used to determine the “magnitude" of two different quaternions. In this case, the interval proposed by the quaternion‐valued is meaningful. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.

show abstract

Dissipativity for a class of quaternion‐valued memristor‐based neutral‐type neural networks with time‐varying delays

Shi

Chen

Zhu

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

In this work, the global dissipativity and exponential dissipativity of quaternion‐valued memristor‐based neutral‐type neural networks (QVNTMNNs) with time‐varying delays are studied. It is worth noting that the QVNTMNN is explored as a single entity without decomposition. Considering the QVNTMNNs as a switching system and utilizing Lyapunov theorem as well as inequality techniques, several sufficient criteria depending on the state‐dependent switching parameters to guarantee global dissipativity and exponential dissipativity of QVNTMNNs with time‐varying delays are obtained in the form of quaternion‐valued linear matrix inequalities (QVLMIs) and corresponding complex‐valued liner matrix inequalities (CVLMIs). Moreover, the positive invariant set, global attractive set, and exponential attractive set of QVNTMNNs with time‐varying delays can also be derived. Finally, two numerical examples are given to substantiate the reliability and validity of our theoretical criteria presented in this work.

show abstract

Dissipativity and exponential state estimation for quaternion-valued memristive neural networks

Cited by 20 publications

References 25 publications

Synchronization in Fixed Time for Reaction–Diffusion Quaternion-Valued NNs with Nonlinear Interconnected Protocol and Its Application

Synchronization in Fixed Time for Reaction–Diffusion Quaternion-Valued NNs with Nonlinear Interconnected Protocol and Its Application

Exponential synchronization and state estimation of inertial quaternion‐valued Cohen‐Grossberg neural networks: Lexicographical order method

Dissipativity for a class of quaternion‐valued memristor‐based neutral‐type neural networks with time‐varying delays

Contact Info

Product

Resources

About