Control of unstable steady states in neutral time-delayed systems

We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between the control strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can successfully stabilize an otherwise unstable steady state.Comment: 11 pages, 8 figure

Mathematical control of complex systems

Copyright © 2013 ZidongWang 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

Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2013 IEEE.In this paper, the synchronization problem is studied for an array of N identical delayed neutral-type neural networks with Markovian jumping parameters. The coupled networks involve both the mode-dependent discrete-time delays and the mode-dependent unbounded distributed time delays. All the network parameters including the coupling matrix are also dependent on the Markovian jumping mode. By introducing novel Lyapunov-Krasovskii functionals and using some analytical techniques, sufficient conditions are derived to guarantee that the coupled networks are asymptotically synchronized in mean square. The derived sufficient conditions are closely related with the discrete-time delays, the distributed time delays, the mode transition probability, and the coupling structure of the networks. The obtained criteria are given in terms of matrix inequalities that can be efficiently solved by employing the semidefinite program method. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 61074129, 61174136 and 61134009, and the Natural Science Foundation of Jiangsu Province of China under Grants BK2010313 and BK2011598

Stabilization of Neutral Systems with Saturating Control Inputs

International audienceThis paper focuses on the stabilization problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimization problems with LMI constraints are therefore proposed to compute stabilizing state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

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

Integral partitioning approach to stability analysis and stabilization of distributed time delay systems

In this paper, the problems of delay-dependent stability analysis and stabilization are investigated for linear continuous-time systems with distributed delay. By introducing an integral partitioning technique, a new form of Lyapunov-Krasovskii functional (LKF) is constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities (LMIs). Based on the criteria, a design algorithm for a state feedback controller is proposed. The results developed in this paper are less conservative than existing ones in the literature, which is illustrated by several examples. © 2011 IFAC.postprintThe 18th World Congress of the International Federation of Automatic Control (IFAC 2011), Milano, Italy, 28 August-2 September 2011. In Proceedings of the 18th IFAC World Congress, 2011, v. 18 pt. 1, p. 5094–509