Chuan-Ke Zhang

Delay-Dependent Stability Criteria for Generalized Neural Networks With Two Delay Components

This paper investigates the delay-dependent stability for generalized continuous neural networks with time-varying delays. A novel Lyapunov-Krasovskii functional (LKF) that considers more information on activation functions of delayed neural networks and delay upper bounds is developed. Simultaneously, most commonly used techniques for treating the derivative of the LKF are reviewed and compared with each other. With the way of introducing slack matrices, those techniques are classified into two categories, including free-weighting matrix (FWM)-based techniques and reciprocally convex combination-based techniques. It is found that the introduced slack matrices play an important role in conservatism reducing and those four types of FWM-based methods lead to same results and are equivalent. Moreover, the obtained criteria are extended to the system with a single time-varying delay. Two numerical examples are given to verify the effectiveness of the proposed method.

Delay-Dependent Robust Load Frequency Control for Time Delay Power Systems

Summary form only given. The usage of communication channels introduces time delays into load frequency control (LFC) schemes. Those delays may degrade dynamic performance, and even cause instability, of a closed-loop LFC scheme. In this paper, a delay-dependent robust method is proposed for analysis/synthesis of a PID-type LFC scheme considering time delays. The effect of the disturbance on the controlled output is defined as a robust performance index (RPI) of the closed-loop system. At first, for a preset delay upper bound, controller gains are determined by minimizing the RPI. Secondly, calculation of the RPIs of the closed-loop system under different delays provides a new way to assess robustness against delays and estimate delay margins. Case studies are based on three-area LFC schemes under traditional and deregulated environments, respectively. The results show that the PID-type controller obtained can guarantee the tolerance for delays less than the preset upper bound and provide a bigger delay margin than the existing controllers do. Moreover, its robustness against load variations and parameter uncertainties is verified via simulation studies.

Exponential synchronization of neural networks with time-varying mixed delays and sampled-data

This paper investigates the problem of exponential synchronization for neural networks with mixed delays using sampled-data feedback control. Lyapunov-Krasovskii functional combining with the input delay approach as well as the improved free-weighting matrix approach are employed to derive several sufficient criteria ensuring the delayed neural networks to be exponentially synchronous. The conditions obtained are dependent not only on the maximum sampling interval but also on the exponential synchronization rate. A numerical example is given to demonstrate the usefulness and merits of the proposed scheme.

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.

Further Results on Delay-Dependent Stability of Multi-Area Load Frequency Control

Further to results reported by Jiang , this paper investigates delay-dependent stability of load frequency control (LFC) emphasizing on multi-area and deregulated environment. Based on Lyapunov theory and the linear matrix inequality technique, a new stability criterion is proposed to improve calculation accuracy and to reduce computation time, which makes it be suitable for handling with multi-area LFC schemes. The interaction of delay margins between different control areas and the relationship between delay margins and control gains are investigated in details. Moreover, usage of delay margins as a new performance index to guide controller design is discussed, including tuning of the controller for a trade-off between delay tolerance and dynamic response, choosing the upper bound of the fault counter of communication channels and the upper bound of sampling period of a discrete realization of the controller. Case studies are carried out based on two-area traditional, two-area and three-area deregulated LFC schemes, all equipped with PID-type controllers, respectively. Simulation studies are given to verify the effectiveness of the proposed method.

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.

Novel stability criteria for recurrent neural networks with time-varying delay ☆

Abstract This paper is concerned with the problem of stability analysis of recurrent neural networks with time-varying delay. An augmented Lyapunov–Krasovskii functional containing a triple integral term and considering more information of activation functions is constructed. Then, Wirtinger-based inequality and two zero-value free-weighting matrix equations are used to deal with the derivative of the Lyapunov–Krasovskii functional. Those treatments lead to less conservatism. A numerical example is given to verify the effectiveness and benefit of the proposed criteria.

Delay-dependent stability analysis of neural networks with time-varying delay

This paper investigates the delay-dependent stability problem of continuous neural networks with a bounded time-varying delay via Lyapunov-Krasovskii functional (LKF) method. This paper focuses on reducing the conservatism of stability criteria by estimating the derivative of the LKF more accurately. Firstly, based on several zero-value equalities, a generalized free-weighting-matrix (GFWM) approach is developed for estimating the single integral term. It is also theoretically proved that the GFWM approach is less conservative than the existing methods commonly used for the same task. Then, the GFWM approach is applied to investigate the stability of delayed neural networks, and several stability criteria are derived. Finally, three numerical examples are given to verify the advantages of the proposed criteria.

Delay-Variation-Dependent Stability of Delayed Discrete-Time Systems

This note is concerned with the stability analysis of linear discrete-time system with a time-varying delay. A generalized free-weighting-matrix (GFWM) approach is proposed to estimate summation terms in the forward difference of Lyapunov functional, and theoretical study shows that the GFWM approach encompasses several frequently used estimation approaches as special cases. Moreover, an augmented Lyapunov functional with a delay-product type term is constructed to take into account delay changing information. As a result, the proposed GFWM approach, together with the augmented Lyapunov functional, leads to a less conservative delay-variation-dependent stability criterion. Finally, numerical examples are given to illustrate the advantages of the proposed criterion.