Global Lagrange Stability Research Articles

Global Lagrange stability analysis of retarded SICNNs

Abstract The stability in the Lagrange sense for cellular neural networks (CNNs) has proven to be one of the effective tools to study multi-stable dynamics of the neural networks. In this article, rather than studying the existence and Lyapunov stability of an equilibrium point we investigate multi-stable dynamics of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and coefficients. This is the first paper that addresses the Lagrange stability for SICNNs. By constructing proper Lyapunov functions and using inequality techniques, we analyze three different types of activation functions, namely, bounded, sigmoid and Lipschitz-like type activation functions. New delay-dependent sufficient criteria are derived to ensure the global Lagrange stability for SICNNs. Furthermore, globally exponentially attractive sets are given for the different activation functions. Finally, an illustrating example with numerical simulations is given to support the theoretical results.

Global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays

This paper focus on the problem of global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays. By choosing a proper variable substitution, an inertial neural network consisting of second-order differential equations can be converted into a first-order differential model. The sufficient conditions of the inertial neural network with neutral delay are derived by constructing suitable Lyapunov-Krasovskii functional candidates, introducing new free weighting matrices, utilizing inequality techniques and analytical method. Through the LMI condition, we analyze the global exponential stability of the delayed inertial neural networks in Lagrange sense. Meanwhile, the global exponential attractive set is also given. Finally, some example is given to illustrate our theoretical results.

Global Lagrange Stability of Inertial Neutral Type Neural Networks with Mixed Time-Varying Delays

This paper deals with the Lagrange stability of inertial neutral type neural networks with mixed time-varying delays. Two different types of activation functions are considered, including bounded and general unbounded activation functions. Under a proper variable transformation, the original inertial system is converted to a first order differential network. Based on Lyapunov method and applying inequality techniques and analytical method, some sufficient criteria are derived to ensure the global Lagrange exponential stability of the addressed neural networks. Moreover, the global exponential attractive sets are established. These results here generalize and improve the earlier publications on inertial neural networks. Finally, some numerical examples with simulations are given to demonstrate the effectiveness of our theoretical results.

Global Lagrange Stability for Takagi-Sugeno Fuzzy Cohen-Grossberg BAM Neural Networks with Time-varying Delays

This paper concerns the globally exponential stability in Lagrange sense for Takagi-Sugeno (T-S) fuzzy Cohen-Grossberg BAM neural networks with time-varying delays. Based on the Lyapunov functional method and inequality techniques, two different types of activation functions which include both Lipschitz function and general activation functions are analyzed. Several sufficient conditions in linear matrix inequality form are derived to guarantee the Lagrange exponential stability of Cohen-Grossberg BAM neural networks with time-varying delays which are represented by T-S fuzzy models. Finally, simulation results demonstrate the effectiveness of the theoretical results.

Global Lagrange stability for inertial neural networks with mixed time-varying delays

This paper concerns with the global Lagrange stability of inertial neural networks with discrete and distributed time-varying delays. By choosing a proper variable substitution, the inertial neural networks can be rewritten as a first-order differential system. Based on the Lyapunov functional method, inequality techniques and analytical method, several sufficient conditions are derived to guarantee the global exponential stability of the inertial neural networks in Lagrange sense. Meanwhile, the global exponential attractive set is also given. Simulation results demonstrate the effectiveness of the theoretical results.

Global lagrange stability of complex‐valued neural networks of neutral type with time‐varying delays

In this article, the problem of global exponential stability in Lagrange sense of neutral type complex‐valued neural networks (CVNNs) with delays is investigated. Two different classes of activation functions are considered, one can be separated into real part and imaginary part, and the other cannot be separated. Based on Lyapunov theory and analytic techniques, delay‐dependent criteria are provided to ascertain the aforementioned CVNNs to be globally exponentially stable GES in Lagrange sense. Moreover, the proposed sufficient conditions are presented in the form of linear matrix inequalities which could be easily checked by Matlab. Finally, two simulation examples are given out to demonstrate the validity of theory results. © 2016 Wiley Periodicals, Inc. Complexity 21: 438–450, 2016

Global Lagrange stability for neutral type neural networks with mixed time-varying delays

In this paper, the global exponential stability in Lagrange sense for neutral type neural networks with mixed time-varying delays is studied. By constructing proper Lyapunov functions and using inequality techniques, new delay-dependent succinct criteria are derived to ensure the global exponential Lagrange stability for the aforementioned neural networks. Meanwhile, globally exponentially attractive sets are given out. The results obtained here are more general than some of existing results. Finally, two examples are presented and analyzed to validate our results.

Global Lagrange stability for neutral-type Cohen–Grossberg BAM neural networks with mixed time-varying delays

The paper discusses global Lagrange stability for a class of Cohen–Grossberg BAM neural networks of neutral-type with multiple time-varying and finite distributed delays by constructing appropriate Lyapunov-like functions. To this end, we first establish a new differential integral inequality for non-autonomous Cohen–Grossberg BAM neural networks with finite distributed delays. By using the new inequality and employing some other inequality techniques, we analyze two different types of activation functions which include both bounded and unbounded activation functions. Some easily verifiable criteria are obtained for global exponential attractive sets in which all trajectories converge. These results can also be applied to analyze monostable as well as multistable and more extensive neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. Finally, some examples with numerical simulations are given and analyzed to verify our results.

Lagrange Stability Analysis for Power Systems with Time-Varying Delays

In this paper, we study the global Lagrange stability for delayed electric power systems. Based on the linear matrix inequality technique, the distinguishing principle and its approach of global Lagrange exponential stability for delayed electric power systems are introduced, which are easily verifiable and have a wider application range. Meanwhile, the estimation of the globally exponentially attractive set (i.e. stable region) is also given out. Finally, an example is given and analyzed to demonstrate our results.

Lyapunov Design of a Dynamic Output Feedback for Systems Linear in Their Unmeasured State Components

We propose a stabilizing output feedback for systems which are linear in their unmeasured state components. We assume weak linear detectability and the knowledge of a globally stabilizing state feedback and of a corresponding Lyapunov function. Our output feedback has an observer-controller structure. It is obtained by following the control Lyapunov function approach. This provides naturally correction terms compared with what would be given by the separation “principle”. Global Lagrange stability is established under the extra assumption that the partial derivatives with respect to the unmeasured state components of the Lyapunov function mentioned above are bounded.

New Criteria for Bounded-Input-Bounded-Output and Asymptotic Stability of Nonlinear Systems

A new approach to the problems of BIBO stability, global Lagrange stability, and global asymptotic stability of nonlinear systems is presented. The three types of stability are analyzed by a unified treatment. Compared to other methods, the timedomain method of analysis used is relatively unrestrictive on the nature of the systems the general nonlinearity considered is not stipulated to be single-valued, continuous, or confined within a linear sector, and the only condition on the linear system is that its impul se re sponse belong to ??? 1. Several criteria are derived, whose application involves the simultaneous solution of two algebraic nonlinear inequalities, which can be implemented by a straightforward graphical construction. The inequalities are expressed in terms of the exact expression (or plot) of the nonlinear characteristic, and the positive and negative areas under the impulse response of the linear system. The theorems on BIBO stability establish quantitative relationships between the numerical bounds on the input and output waveforms. A number of examples on the various theorems are presented, in which the present results are demonstrated to furnish information about the system stability which cannot be obtained from other criteria such as the Popov and Circle Theorems.