Zixin Liu

Stabilization analysis for discrete-time systems with time delay

The stabilization problem for a class of discrete-time systems with time-varying delay is investigated. By constructing an augmented Lyapunov function, some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality (LMI) technique. When norm-bounded parameter uncertainties appear in the delayed discrete-time system, a delay-dependent robust exponential stabilization criterion is also presented. All of the criteria obtained in this paper are strict linear matrix inequality conditions, which make the controller gain matrix can be solved directly. Three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results.

Improved exponential stability criteria for discrete-time neural networks with time-varying delay

The problem of robust exponential stability for a class of discrete-time recurrent neural networks with time-varying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii functional, some new delay-dependent stable criteria are obtained. These criteria are formulated in the forms of linear matrix inequality (LMI). Compared with some previous results, the new conditions obtained in this paper are less conservative. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

Improved Robust Stability Criteria of Uncertain Neutral Systems with Mixed Delays

The problem of robust stability for a class of neutral control systems with mixed delays is investigated. Based on Lyapunov stable theory, by constructing a new Lyapunov-Krasovskii function, some new stable criteria are obtained. These criteria are formulated in the forms of linear matrix inequalities (LMIs). Compared with some previous publications, our results are less conservative. Simulation examples are presented to illustrate the improvement of the main results.

New Improved Exponential Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

The robust stability of uncertain discrete-time recurrent neural networks with time-varying delay is investigated. By decomposing some connection weight matrices, new Lyapunov-Krasovskii functionals are constructed, and serial new improved stability criteria are derived. These criteria are formulated in the forms of linear matrix inequalities (LMIs). Compared with some previous results, the new results are less conservative. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

NOVEL EXPONENTIAL STABILITY CONDITIONS FOR A CLASS OF INTERVAL PROJECTION NEURAL NETWORKS

In this paper, a class of interval projection neural networks for solving quadratic programming problems are investigated. By using Gronwall inequality and constructing appropriate Lyapunov functionals, several novel conditions are derived to guarantee the exponential stability of the equilibrium point. Compared with previous results, the conclusions obtained here are suitable not only to convex quadratic programming problems but also to degenerate quadratic programming problems, and the conditions are more weaker than the earlier results reported in the literature. In addition, one numerical example is discussed to illustrate the validity of the main results.

A New Delayed Projection Neural Network for Solving Linear Variational Inequalities and Quadratic Optimization Problems

For solving linear variational inequalities(LVIs) and quadratic optimization problems(QOPs), a new delayed projection neural network is proposed in this paper. And some sufficient conditions ensuring exponential stability are obtained via constructing appropriate Lyapunov functionals. As a special case, a matrix constraint is considered too. In this case, by dividing the network state variables into subgroups according to the character of the activation functions, some more compact sufficient conditions ensuring exponential stability are obtained, and these conditions are only relate to some blocks of the interconnection matrix. One numerical example will be presented, to show the effectiveness of the main results.

Exponentially Stable Conditions of Parametric Uncertainty Impulsive Switched Systems with Time Delay

In this paper, a class of linear switched systems with time delays is investigated. At the same time, the impulsive effects and parametric uncertainty assumed to be norm-bounded are considered. Some novel exponentially stable criteria are obtained by constructing appropriate Lyapunov-Krasovskii functional. The validity of the results is shown by one numerical example.

Exponential Synchronization of a Class of Delayed Stochastic Neural Networks with Impulsive Effects

In this paper, the mean square exponential synchronization of a class of delayed stochastic neural networks with impulsive effects is investigated. By using Gronwall-Bellman inequality, stochastic analysis and inequality technique, some sufficient conditions ensuring the mean square exponential synchronization are obtained.