Exponential stabilization of fractional-order continuous-time dynamic systems via event-triggered impulsive control

Exponential stabilization of fractional-order continuous-time dynamic systems via eventtriggered impulsive control (EIC) approach is investigated in this paper. Nonlinear and linear fractional-order continuous-time dynamic systems are studied, respectively. The impulsive instants are determined by some given event-triggering function and event-triggering condition, which are dependent on the state of the systems. Sufficient conditions on exponential stabilization for nonlinear and linear cases are presented, respectively. Moreover, the Zeno-behavior of impulsive instants is excluded. Finally, the validity of theoretical results are also illustrated by some numerical simulation examples including the synchronization control of fractional-order jerk chaotic system

Improved synchronization analysis of competitive neural networks with time-varying delays

Synchronization and control are two very important aspects of any dynamical systems. Among various kinds of nonlinear systems, competitive neural network holds a very important place due to its application in diverse fields. The model is general enough to include, as subclass, the most famous neural network models such as competitive neural networks, cellular neural networks and Hopfield neural networks. In this paper, the problem of feedback controller design to guarantee synchronization for competitive neural networks with time-varying delays is investigated. The goal of this work is to derive an existent criterion of the controller for the exponential synchronization between drive and response neutral-type competitive neural networks with time-varying delays. The method used in this brief is based on feedback control gain matrix by using the Lyapunov stability theory. The synchronization conditions are given in terms of LMIs. To the best of our knowledge, the results presented here are novel and generalize some previous results. Some numerical simulations are also represented graphically to validate the effectiveness and advantages of our theoretical results

Polybius and the anger of the Romans

In this paper, incremental exponential asymptotic stability of a class of switched Carathéodory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients between these norms. This model is rather general and includes the case of staircase switching signals as a special case. Sufficient conditions are derived for incremental stability allowing for the system to be incrementally exponentially asymptotically stable even if some of its modes are unstable in some time periods. Numerical examples on switched linear systems with periodic switching and on the synchronization of switched networks of nonlinear systems are used to illustrate the theoretical results

Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling

In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.Comment: 12 pages, 18 figure

Transverse exponential stability and applications

We investigate how the following properties are related to each other: i)-A manifold is "transversally" exponentially stable; ii)-The "transverse" linearization along any solution in the manifold is exponentially stable; iii)-There exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property

Nonlinearly driven transverse synchronization in coupled chaotic systems

Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When only two maps are considered we always find that the critical coupling $\epsilon_l$ for chaotic synchronization can be predicted within a linear analysis by the vanishing of the transverse Lyapunov exponent $\lambda_T$. However, major differences between transitions driven by linear or nonlinear mechanisms are revealed by the dynamics of the transient toward the synchronized state. As a representative example of extended systems a one dimensional lattice of chaotic maps with power-law coupling is considered. In this high dimensional model finite amplitude instabilities may have a dramatic effect on the transition. For strong nonlinearities an exponential divergence of the synchronization times with the chain length can be observed above $\epsilon_l$, notwithstanding the transverse dynamics is stable against infinitesimal perturbations at any instant. Therefore, the transition takes place at a coupling $\epsilon_{nl}$ definitely larger than $\epsilon_l$ and its origin is intrinsically nonlinear. The linearly driven transitions are continuous and can be described in terms of mean field results for non-equilibrium phase transitions with long range interactions. While the transitions dominated by nonlinear mechanisms appear to be discontinuous.Comment: 29 pages, 14 figure

State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: The discrete-time case

Copyright [2009] 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.This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes