Proposed Linear Matrix Inequality Conditions Research Articles

Robust Stabilization of Discrete‐Time Systems with Time‐Varying Delay: An LMI Approach

Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete‐time systems with time‐varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter‐dependent Lyapunov‐Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

New criteria on global robust stability of Cohen–Grossberg neural networks with time-varying delays

This paper considers the problem of robust stability analysis of Cohen–Grossberg neural networks with time-varying delays and norm-bounded parameter uncertainties. The activation functions are assumed to be bounded and globally Lipschitz continuous. Both the monotonic increasing and non-monotonic increasing activations are considered. In terms of linear matrix inequalities (LMIs), sufficient conditions are obtained by using the Lyapunov–Krasovskii method, which guarantee the existence, uniqueness and global robust asymptotic stability of the equilibrium point of the delayed Cohen–Grossberg neural network. It is theoretically established that the derived LMI conditions are less conservative than certain existing ones in the literature. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

Some criteria for robust stability of Cohen–Grossberg neural networks with delays

This paper considers the problem of robust stability of Cohen–Grossberg neural networks with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Comparisons between our results and previous results admits our results establish a new set of stability criteria for delayed Cohen–Grossberg neural networks. Numerical examples are given to illustrate the effectiveness of our results.

Global robust exponential stability of delayed neural networks

In this paper, the global robust exponential stability of interval neural networks with time delays is investigated. As far as we are aware only, few papers deals with the interval neural networks and focus on the robust exponential stability. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally robust exponentially stable. The proposed LMI conditions can be checked easily by a recently developed algorithms solving LMIs.

A new approach to exponential stability analysis of neural networks with time-varying delays

This paper considers the problem of exponential stability analysis of neural networks with time-varying delays. The activation functions are assumed to be globally Lipschitz continuous. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally exponentially stable. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the reduced conservativeness of the proposed results.

Delay-dependent exponential stability for a class of neural networks with time delays

This paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type. In terms of a linear matrix inequality (LMI), a sufficient condition guaranteeing the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed. This condition is dependent on the size of the time delay, which is usually less conservative than delay-independent ones. The proposed LMI condition can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.