Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

International audienc

Global Stability Analysis for Periodic Solution in Discontinuous Neural Networks with Nonlinear Growth Activations

This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential inclusion theory, matrix theory, and generalized Lyapunov approach, a general result is derived which ensures the existence and global asymptotical stability of a unique periodic solution for such neural networks. The obtained results can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also show that Forti's conjecture for discontinuous neural networks with nonlinear growth activations is true

Global Stability Analysis for Periodic Solution in Discontinuous Neural Networks with Nonlinear Growth Activations

This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential inclusion theory, matrix theory, and generalized Lyapunov approach, a general result is derived which ensures the existence and global asymptotical stability of a unique periodic solution for such neural networks. The obtained results can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also show that Forti's conjecture for discontinuous neural networks with nonlinear growth activations is true.</p

Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters

The exponential stability issue for a class of stochastic neural networks (SNNs) with Markovian jump parameters, mixed time delays, and α-inverse Hölder activation functions is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Firstly, based on Brouwer degree properties, the existence and uniqueness of the equilibrium point for SNNs without noise perturbations are proved. Secondly, by applying the Lyapunov-Krasovskii functional approach, stochastic analysis theory, and linear matrix inequality (LMI) technique, new delay-dependent sufficient criteria are achieved in terms of LMIs to ensure the SNNs with noise perturbations to be globally exponentially stable in the mean square. Finally, two simulation examples are provided to demonstrate the validity of the theoretical results

Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results

A One-Layer Recurrent Neural Network for Solving Pseudoconvex Optimization with Box Set Constraints

A one-layer recurrent neural network is developed to solve pseudoconvex optimization with box constraints. Compared with the existing neural networks for solving pseudoconvex optimization, the proposed neural network has a wider domain for implementation. Based on Lyapunov stable theory, the proposed neural network is proved to be stable in the sense of Lyapunov. By applying Clarke’s nonsmooth analysis technique, the finite-time state convergence to the feasible region defined by the constraint conditions is also addressed. Illustrative examples further show the correctness of the theoretical results

Stability in Switched Cohen-Grossberg Neural Networks with Mixed Time Delays and Non-Lipschitz Activation Functions

The stability for the switched Cohen-Grossberg neural networks with mixed time delays and α-inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay-dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results

Bistatic Forward-Looking SAR Moving Target Detection Method Based on Joint Clutter Cancellation in Echo-Image Domain with Three Receiving Channels

In bistatic forward-looking synthetic aperture radar (BFSAR) ground moving target detection (GMTD), the suppression of the strong and heterogeneous ground clutter is one of the most crucial and challenging issues. Due to the bistatic forward-looking mode and long observation time, Doppler ambiguity, range and Doppler cells migration and non-stationary characteristics will exist in clutter receives, which leads to severe performance degradation of the traditional method. Hence, this paper proposes a GMTD method based on joint clutter cancellation in echo-image domain for BFSAR to achieve effective GMTD in heterogeneous BFSAR clutter. First, the pre-filtering and keystone transform are applied to suppress Doppler ambiguity and correct range cell migration, respectively. Then, time-division space-time adaptive clutter cancellation is adopted to suppress clutter at the first time in the echo domain, which can eliminate the effect of the migration of Doppler cells. However, its performance will be severely degraded due to the strong non-stationary characteristic of BFSAR clutter. Finally, adaptive displaced phase center antenna is exploited to suppress the residual non-stationary BFSAR clutter in image domain. Experimental results have shown that the strong non-stationary clutter of BFSAR has been sufficiently suppressed by the proposed method and the SCNR provided is enough to detect a moving target well