Robust passivity and passification of stochastic fuzzy time-delay systems

The official published version can be obtained from the link below.In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.This work was supported by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers 200802861044, the National Natural Science Foundation of China under Grant 60804028 and the Royal Society of the United Kingdom

On passivity and passification of stochastic fuzzy systems with delays: The discrete-time case

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Takagi–Sugeno (T-S) fuzzy models, which are usually represented by a set of linear submodels, can be used to describe or approximate any complex nonlinear systems by fuzzily blending these subsystems, and so, significant research efforts have been devoted to the analysis of such models. This paper is concerned with the passivity and passification problems of the stochastic discrete-time T-S fuzzy systems with delay. We first propose the definition of passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented, ensuring the passivity performance of the T-S fuzzy models. Finally, based on this criterion, state feedback controller is designed, and several criteria are obtained to make the closed-loop system passive in the sense of expectation. The results acquired in this paper are delay dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are also provided to demonstrate the effectiveness and feasibility of our criteria.This work was supported in part by the Royal Society Sino–British Fellowship Trust Award of the U.K., by the National Natural Science Foundation of China under Grant 60804028, by the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers in China under Grant 200802861044, and by the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China

Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays

The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI)

STABILITY, FINITE-TIME STABILITY AND PASSIVITY CRITERIA FOR DISCRETE-TIME DELAYED NEURAL NETWORKS

In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology

Finite-time passivity for neutral-type neural networks with time-varying delays – via auxiliary function-based integral inequalities

In this paper, we investigated the problem of the finite-time boundedness and finitetime passivity for neural networks with time-varying delays. A triple, quadrable and five integral terms with the delay information are introduced in the new Lyapunov–Krasovskii functional (LKF). Based on the auxiliary integral inequality, Writinger integral inequality and Jensen’s inequality, several sufficient conditions are derived. Finally, numerical examples are provided to verify the effectiveness of the proposed criterion. There results are compared with the existing results.&nbsp

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature