Asymptotic stability of differential systems of neutral type (original) (raw)
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An improved stability criterion for a class of neutral differential equations
Applied Mathematics Letters
This work gives an improved criterion for asymptotical stability of a class of neutral differential equations. By introducing a new Lyapunov functional, we avoid the use of the stability assumption on the main operators and derive a novel stability criterion given in terms of a LMI, which is less restricted than that given by Park [J.H. Park, Delay-dependent criterion for asymptotic stability of a class of neutral equations, Appl. Math. Lett. 17 (2004) 1203–1206] and Sun et al. [Y.G. Sun, L. Wang, Note on asymptotic stability of a class of neutral differential equations, Appl. Math. Lett. 19 (2006) 949–953].
Exponential Convergence Estimates for a Single Neuron System of Neutral-Type
Ieee Transactions on Neural Networks and Learning Systems, 2014
The future behavior of a dynamical system is determined by its initial state or initial function. Nontrivial neuron system involving adaptive learning corresponds to the memorization of initial information. In this paper, exponential estimates and sufficient conditions for the exponential stability of a single neuron system of neutral-type are studied. Of particular importance is the fact that exponential convergence guarantees that this system is capable of memorizing initial functions. Furthermore, this system is also capable of conveying much more information with respect to the initial functions memorized by neuron system with time delay. The proofs follow some new results on nonhomogeneous difference equations evolving in continuous-time combined with the Lyapunov-Krasovskii functional and the descriptor system approach. The exponential stability conditions are expressed in terms of a linear matrix inequality, which lead to less restrictive and less conservative exponential estimates.
Stability and Convergence Analysis for a Class of Neural Networks
IEEE Transactions on Neural Networks, 2011
A systematic and general method that proves state boundedness and convergence to nonzero equilibrium for a class of nonlinear passive systems with constant external inputs is developed. First, making use of the method of linear-timevarying approximations, the boundedness of the nonlinear system states is proven. Next, taking advantage of the passivity property, it is proven that a suitable switching storage function can be always obtained to show convergence to the nonzero equilibrium by using LaSalle's Invariance Principle. Numerical and simulation results illustrate the proposed theoretical analysis.
In this paper, exponential estimates and sufficient criteria for the exponential stability of neutral-type neural networks with multiple delays are given. First, because of the key role of the difference equation part of the neutral-type neural networks with multiple delays, some novel results concerning exponential estimates for non-homogeneous difference equations evolving in continuous time are derived. Then, by constructing several different Lyapunov-Krasovskii functionals combined with a descriptor transformation approach at some cases, several novel global and exponential stability conditions are presented and expressed in terms of linear matrix inequalities (LMIs), and the obtained results are less conservative and restrictive than the known results. Some numerical examples are also given to show their effectiveness and advantages over others.
Advances in Difference Equations
In this paper we consider a standard class of the neural networks and propose an investigation of the global asymptotic stability of these neural systems. The main aim of this investigation is to define a novel Lyapunov functional having quadratic-integral form and use it to reach a stability criterion for the under study neural networks. Since some fundamental characteristics, such as nonlinearity, including time-delays and neutrality, help us design a more realistic and applicable model of neural systems, we will use all of these factors in our neural dynamical systems. At the end, some numerical simulations are presented to illustrate the obtained stability criterion and show the essential role of the time-delays in appearance of the oscillations and stability in the neural networks.
Stability analysis of neutral type systems in
2015
The asymtoptic stability properties of neutral type systems are studied mainly in the critical case when the exponential stability is not possible. We consider an op-erator model of the system in Hilbert space and use recent results on the existence of a Riesz basis of invariant finite-dimensional subspaces in order to verify its dis-sipativity. The main results concern the conditions of asymptotic non exponential stability. We show that the property of asymptotic stability is not determinated only by the spectrum of the system but essentially depends on the geometric spec-tral characteristic of its main neutral term. Moreover, we present an example of two systems of neutral type which have both the same spectrum in the open left-half plane and the main neutral term but one of them is asymptotically stable while the other is unstable.
Global Asymptotic Stability of Cohen–Grossberg Neural Networks of Neutral Type
Journal of Mathematical Sciences, 2015
Sufficient conditions for existence and global asymptotic stability of a unique equilibrium point of a Cohen-Grossberg neural network of neutral type are obtained. An example is given. Отримано достатнi умови iснування та глобальної стiйкостi єдиної точки рiвноваги для нейронної мережi Коена-Гроссберга нейтрального типу.