Robust exponential stability of switched interval interconnected systems with unbounded delay

et al. 2022

Self Cite

PurposeThe purpose of this paper is to study the dynamic behavior of complex-valued switched grey neural network models (SGNMs) with distributed delays when the system parameters and external input are grey numbers.Design/methodology/approachFirstly, by using the properties of grey matrix, M-matrix theory and Homeomorphic mapping, the existence and uniqueness of equilibrium point of the SGNMs were discussed. Secondly, by constructing a proper Lyapunov functional and using the average dwell time approach and inequality technique, the robust exponential stability of the SGNMs under restricted switching was studied. Finally, a numerical example is given to verify the effectiveness of the proposed results.FindingsSufficient conditions for the existence and uniqueness of equilibrium point of the SGNMs have been established; sufficient conditions for guaranteeing the robust stability of the SGNMs under restricted switching have been obtained.Originality/value(1) Different from asymptotic stability, the exponential stability of SGNMs which include grey parameters and distributed time delays will be investigated in this paper, and the exponential convergence rate of the SGNMs can also be obtained; (2) the activation functions, self-feedback coefficients and interconnected matrices are with different forms in different subnetworks; and (3) the results obtained by LMIs approach are complicated, while the proposed sufficient conditions are straightforward, which are conducive to practical applications.

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust stability analysis of switched grey neural network models with distributed delays over C

Zhang

et al. 2022

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“…Definition (see [36,37]). It is supposed that ( 1 , 2 ) denotes the switching numbers on time-interval ( 1 , 2 ), here 1 > 0.…”

Section: Assumption Each Function ℎ (⋅) Is Globally Lipschitz Withmentioning

confidence: 99%

Robust Exponential Stability of Switched Complex‐Valued Neural Networks with Interval Parameter Uncertainties and Impulses

Peng

et al. 2018

Complexity

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In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example.

“…Furthermore, from the point of view of control, multicontroller switching is an effective way to deal with complex systems. It is well-known that time delays are inevitable in a practical control design which usually leads to unsatisfactory performances and the stability of the dynamic systems may even be destroyed with the increase of delays [30][31][32][33][34][35]. Attributing to the interaction among the discrete dynamics, continuous dynamics, and time delays, the behaviors of delayed SNNs are very complicated.…”

Section: Introductionmentioning

confidence: 99%

Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

Peng

et al. 2018

Complexity

Self Cite

In this paper, the stability of switched neural networks (SNNs) with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature.