Min Wu

Stability Analysis for Neural Networks With Time-Varying Interval Delay

This letter is concerned with the stability analysis of neural networks (NNs) with time-varying interval delay. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay/interval-dependent stability criteria for NNs with time-varying interval delay are proposed. Numerical examples are given to demonstrate the effectiveness and the merits of the proposed method.

Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay

The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.

Improving Disturbance-Rejection Performance Based on an Equivalent-Input-Disturbance Approach

This paper presents a new method of improving the disturbance-rejection performance of a servo system based on the estimation of an equivalent input disturbance (EID). First, the concept of EID is defined. Next, the configuration of an improved servo system employing the new disturbance-estimation method is described. Then, a method of designing a control law employing a disturbance estimate is explained. Finally, the speed control of a rotational control system is used to demonstrate the validity of the method, and some design guidelines are presented.

Delay-dependent state estimation for delayed neural networks

In this letter, the delay-dependent state estimation problem for neural networks with time-varying delay is investigated. A delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. The proposed method is based on the free-weighting matrix approach and is applicable to the case that the derivative of a time-varying delay takes any value. An algorithm is presented to compute the state estimator. Finally, a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones.

New results on stability analysis for systems with discrete distributed delay

The integral inequality technique is widely used to derive delay-dependent conditions, and various integral inequalities have been developed to reduce the conservatism of the conditions derived. In this study, a new integral inequality was devised that is tighter than existing ones. It was used to investigate the stability of linear systems with a discrete distributed delay, and a new stability condition was established. The results can be applied to systems with a delay belonging to an interval, which may be unstable when the delay is small or nonexistent. Three numerical examples demonstrate the effectiveness and the smaller conservatism of the method.

Stability analysis of systems with time-varying delay via relaxed integral inequalities

Abstract This paper investigates the stability of linear systems with a time-varying delay. The key problem concerned is how to effectively estimate single integral term with time-varying delay information appearing in the derivative of Lyapunov–Krasovskii functional. Two novel integral inequalities are developed in this paper for this estimation task. Compared with the frequently used inequalities based on the combination of Wirtinger-based inequality (or Auxiliary function-based inequality) and reciprocally convex lemma, the proposed ones can provide smaller bounding gap without requiring any extra slack matrix. Four stability criteria are established by applying those inequalities. Based on three numerical examples, the advantages of the proposed inequalities are illustrated through the comparison of maximal admissible delay bounds provided by different criteria.

Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity

This paper investigates delay-dependent stability for continuous neural networks with a time-varying delay. This paper aims at deriving a new stability criterion, considering tradeoff between conservativeness and calculation complexity. A new Lyapunov-Krasovskii functional with simple augmented terms and delay-dependent terms is constructed, and its derivative is estimated by several techniques, including free-weighting matrix and inequality estimation methods. Then, the influence of the techniques used on the conservativeness and the complexity is analyzed one by one. Moreover, useful guidelines for improving criterion and future work are briefly discussed. Finally, the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples.

Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality

This paper is concerned with global exponential stability problem for a class of neural networks with time-varying delays. Using a new proposed inequality called free-matrix-based integral inequality, a less conservative criterion is proposed, which is expressed by linear matrix inequalities. Two numerical examples are given to show the effectiveness and superiority of the obtained criterion.

Stability analysis of generalized neural networks with time-varying delays via a new integral inequality

This paper focuses on the delay-dependent stability of a class of generalized neural networks (NNs) with time-varying delays. A free-matrix-based inequality is presented by introducing a set of slack variables, which encompasses the Wirtinger-based inequality as a special case. Then, by constructing a suitable Lyapunov-Krasovskii functional and utilizing the new inequality to bound the derivative of the Lyapunov-Krasovskii functional, some sufficient conditions are derived to assure the stability of the considered neural networks. Three numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed method.

Integrated Hybrid-PSO and Fuzzy-NN Decoupling Control for Temperature of Reheating Furnace

This paper presents an integrated method of intelligent decoupling control as a solution to the problem of adjusting the zone temperatures in a regenerative pusher-type reheating furnace. First, a recurrent neural network (NN) for estimating the zone temperatures and a heat transfer model for predicting billet temperatures are built based on data from actual furnace operations. Next, a decoupling strategy in combination with a fuzzy NN is used to control the zone temperatures. The architecture of the controller is based on a fuzzy c-means clustering approach; and the weights are optimized by a hybrid particle swarm optimization (HPSO) algorithm, which integrates the global optimization of density-based selection and the precise search of clonal expansion in an immune system with the fast local search of particle swarm optimization. HPSO is also used to optimize the zone temperature settings to minimize three items: fuel consumption, the temperature gradient within a billet, and the error between the mean and target temperatures of a billet at the furnace exit. The results of actual runs demonstrate the validity of this method.