Narrow Results

This letter considers uncertain Lur'e systems of neutral type with sector and slope restrictions. By constructing a new Lyapunov functional, a novel delay-dependent criterion for absolute stability is derived in terms of linear matrix inequalities (LMIs). Two numerical examples are illustrated to show the effectiveness of the proposed method.

This paper deals with the problem of master-slave synchronization for uncertain Lur'e systems via time-varying delay feedback control. The parametric uncertainty is assumed to be norm bounded. Several new and sufficient conditions are presented such that the uncertain Lur'e master and slave systems are synchronous for all admissible uncertainties. These synchronization criteria are dependent on the size of time delay, which can be expressed by means of matrix inequalities. The adopted method is based on defining a new Lyapunov–Krasovskii function and using some inequalities techniques. Our results obtained here extend and improve some previously related results. Finally, two numerical examples are provided to demonstrate the applications of our proposed results.

A method for estimating the parameters of continuous-time Lur'e systems is proposed. The method is based on the derivation of an approximate, discrete-time model, in the form of a scalar difference equation, which can directly be used for data fitting. The discretization can be obtained through any (fixed-step) integration scheme: in the paper, the performance of a simple scheme (the trapezoidal rule) and a more complex one (the Runge–Kutta rule) are compared. The method, tested on three different examples (Duffing system, an electrical circuit and Chua's circuit), proves to be capable of obtaining a rapid parameter estimation with an acceptable level of accuracy.

This paper deals with the master-slave synchronization problem of Lur'e systems based on time-varying delay feedback control. The time-varying delay is only assumed to be bounded. Delay-dependent conditions are derived such that the controlled slave system can track the master system. The synchronization criteria are expressed in terms of linear matrix inequality, which can be checked readily by using some standard numerical packages. A simulation example is provided to demonstrate the effectiveness of the proposed approach.

This paper deals with master–slave synchronization for Lur'e systems subject to a more general sector condition by using time delay feedback control. A new Lyapunov–Krasovskii functional and a new Lur'e–Postnikov Lyapunov functional are proposed to obtain some new delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs). These criteria cover some existing results as their special cases. An example shows that the result derived in this paper significantly improves some existing ones.

This paper investigates the effects of coupling delays on synchronization in Lur'e complex dynamical networks. Every identical node in the network can be represented as a Lur'e system. Based on Lyapunov–Krasovskii functionals and Lur'e–Postnikov Lyapunov functionals, some delay-dependant synchronization criteria are derived by employing a delay decomposition approach. A Lur'e complex dynamical network with Chua's circuit nodes and one numerical example are given to illustrate the effectiveness of the synchronization criteria.

Based on some essential concepts of fractional calculus and the theorem related to the fractional extension of Lyapunov direct method, we present in this paper a synchronization scheme of fractional-order Lur’e systems. A quadratic Lyapunov function is chosen to derive the synchronization criterion. The derived criterion is a suffcient condition for the asymptotic stability of the error system, formulated in the form of linear matrix inequality (LMI). The controller gain can be achieved by solving the LMI. The proposed scheme is illustrated for fractional-order Chua’s circuits and fractional-order four-cell CNN. Numerical results, which agree well with the proposed theorem, are given to show the effectiveness of this scheme.