Global Exponential Stability Result Research Articles

Further improved global exponential stability result for neural networks with time-varying delay

Further improved global exponential stability result for neural networks with time-varying delay

PD-Like Regulation of Mechanical Systems With Prescribed Bounds of Exponential Stability: The Point-to-Point Case

This letter discusses an extension of the famous PD regulator implementing point to point motions with prescribed exponential rates of convergence. This is achieved by deriving a novel global exponential stability result, dealing with mechanical systems evolving on uni-dimensional invariant manifolds of the configuration space. The construction of closed loop controllers enforcing the existence of such manifolds is then discussed. Explicit upper and lower bounds of convergence are provided, and connected to the gains of the closed loop controller. Simulations are carried out, assessing the effectiveness of the controller and the tightness of the exponential bounds.

Stability analysis of almost periodic solutions for discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays

Abstract This paper aims to discuss a class of discontinuous bidirectional associative memory (BAM) neural networks with discrete and distributed delays. By using the set-valued map, differential inclusions theory and fundamental solution matrix, the existence of almost-periodic solutions for the addressed neural network model is firstly discussed under some new conditions. Subsequently, based on the non-smooth analysis theory with Lyapunov-like strategy, the global exponential stability result of the almost-periodic solution for the proposed neural network system is also established without using any additional conditions. The results achieved in the paper extend some previous works on BAM neural networks to the discontinuous case and it is worth mentioning that it is the first time to investigate the almost-periodic dynamic behavior for the BAM neural networks like the form in this paper. Finally, in order to demonstrate the effectiveness of the theoretical schemes, simulation results of two topical numerical examples are delineated.

Recursive dynamics in a class of systems on q-timescales with unbounded delays

This work deals with a class of retarded equations on q-time scales which involves unbounded delays. A global exponential stability result is obtained and a dynamic of the recursive steps due to the delay function is discussed. A formal representation of natural numbers with respect to an unbounded delay function is featured with an asymptotic behavior of the recursion in an extended class of retarded equations.

Hybrid global exponential stabilization on [formula omitted

We propose a central synergistic hybrid approach for global exponential stabilization on the Special Orthogonal group SO(3). We introduce a new switching concept relying on a central family of (possibly) non-differentiable potential functions that enjoy the following properties: (1) being quadratic (as well as their gradients) with respect to the Euclidean attitude distance, and (2) being synergistic with respect to the gradient’s singular and/or critical points. The proposed approach is used to solve the attitude tracking problem, leading to global exponential stability results.

New global exponential stability results for a memristive neural system with time-varying delays

Recent research in memristor–CMOS neuromorphic learning systems has led to the practical realization of neuro-inspired learning architectures. At present, the deep understanding of nonlinear dynamical mechanisms governing memristive neural systems is still an open issue. In this paper, the global exponential stability problem is investigated for a class of memristive neural systems with time-varying delays. By employing comparison principle, some novel global exponential stability results are derived. These stability conditions also improve upon some existing results. In addition, the obtained results are convenient to estimate the exponential convergence rate. These theoretical studies are very useful in analyzing the composite behavior of complex memristor circuits.

Global exponential stability result for complex valued hysteretic neuron model

A mathematical model of artificial neural networks with hysteresis is formulated using neutral delay differential equations. Hysteresis modifies the systems such that they cannot produce unique output for any given input, rather output is produced based on the past history of the system. Motivated by the applications of complex valued neural networks in artificial neural networks, we studied the global dynamics of complex valued neural network with hysteresis. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the neural delay. In this paper continuous hysteresis neuron model has been used to arrive at the sufficient condition for global exponential stability of a unique equilibrium. The hypothetical insight has been successfully applied and verified using relevant numerical examples.

New global exponential stability result to a general Cohen–Grossberg neural networks with multiple delays

In this paper, we first discuss the existence of an equilibrium point to a general Cohen–Grossberg neural networks with multiple delays by means of using degree theory and linear matrix inequality (LMI) technique. Then by applying the existence result of an equilibrium point, linear matrix inequality technique and constructing a Lyapunov functional, we study the global exponential stability of equilibrium solution to the Cohen–Grossberg neural networks. Compared with known results, our results of global exponential stability of equilibrium point are new. In our results, the hypothesis for differentiability in existing papers on the behaved functions is removed and the hypotheses for boundedness and monotonicity in existing papers on the activation functions are also removed.

Periodic solution to Cohen–Grossberg BAM neural networks with delays on time scales

In this paper, we investigate first the existence and uniqueness of periodic solution in a general Cohen–Grossberg BAM neural networks with delays on time scales by means of contraction mapping principle. Then by using the existence result of periodic solution and constructing a Lyapunov functional, we discuss the global exponential stability of periodic solution for above neural networks. In the last section, we also give examples to demonstrate the validity of our global exponential stability result of the periodic solution for above neural networks.

Global exponential stability of interval general BAM neural networks with reaction–diffusion terms and multiple time-varying delays

In this paper, we first discuss the existence and uniqueness of the equilibrium point of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays by means of using degree theory. Then by applying the existence result of an equilibrium point and constructing a Lyapunov functional, we discuss global exponential stability for above neural networks. In the last section, we also give an example to demonstrate the validity of our global exponential stability result for above neural network.

On existence and global exponential stability of periodic solution of two-neuron networks with time-varying delays

This Letter presents new sufficient conditions for the existence and global exponential stability of periodic solution of two-neuron networks with time-varying delays. Our approach is based on the differential inequalities. The results are shown to generalize the previous existence and global exponential stability results derived in the literature. Numerical simulations are given at the end of the Letter.

On Global Exponential Stability of Discrete-Time Hopfield Neural Networks with Variable Delays

Global exponential stability of a class of discrete-time Hopfield neural networks with variable delays is considered. By making use of a difference inequality, a new global exponential stability result is provided. The result only requires the delay to be bounded. For this reason, the result is milder than those presented in the earlier references. Furthermore, two examples are given to show the efficiency of our result.

Harmless delays for global exponential stability of Cohen–Grossberg neural networks

In this paper, the Cohen–Grossberg neural networks with time delays are considered without assuming any symmetry of connection matrix and differentiability of the activation functions. By constructing a novel Lyapunov functional, new sufficient criteria for the existence of a unique equilibrium and global exponential stability of the network are derived. These criteria are all independent of the magnitudes of delays, and so the delays under these conditions are harmless. Those results are shown to generalize the previous global exponential stability results derived in the literature.

Functional central limit theorems for a large network in which customers join the shortest of several queues

We consider N single server infinite buffer queues with service rate β. Customers arrive at rate Nα, choose L queues uniformly, and join the shortest. We study the processes Open image in new window for large N, where RNt(k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We consider certain Hilbert spaces with the weak topology. First, we prove a functional central limit theorem (CLT) under the a priori assumption that the initial data RN0 satisfy the corresponding CLT. We use a compactness-uniqueness method, and the limit is characterized as an Ornstein-Uhlenbeck (OU) process. Then, we study the RN in equilibrium under the stability condition α<β, and prove a functional CLT with limit the OU process in equilibrium. We use ergodicity and justify the inversion of limits lim N→∞ lim t→∞= lim t→∞ lim N→∞ by a compactness-uniqueness method. We deduce a posteriori the CLT for RN0 under the invariant laws, an interesting result in its own right. The main tool for proving tightness of the implicitly defined invariant laws in the CLT scaling and ergodicity of the limit OU process is a global exponential stability result for the nonlinear dynamical system obtained in the functional LLN limit.

GLOBAL EXPONENTIAL STABILITY IN HOPFIELD AND BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH TIME DELAYS

Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.

Global stability of a class of continuous-time recurrent neural networks

This paper investigates global asymptotic stability (GAS) and global exponential stability (GES) of a class of continuous-time recurrent neural networks. First, we introduce a necessary and sufficient condition for the existence and uniqueness of equilibrium of the neural networks with Lipschitz continuous activation functions. Next, we present two sufficient conditions to ascertain the GAS of the neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions. We then give two GES conditions for the neural networks whose activation functions may not be monotone nondecreasing. We also provide a Lyapunov diagonal stability condition, without the nonsingularity requirement for the connection weight matrices, to ascertain the GES of the neural networks with globally Lipschitz continuous and monotone nondecreasing activation functions. This Lyapunov diagonal stability condition generalizes and unifies many of the existing GAS and GES results. Moreover, two higher exponential convergence rates are estimated.