Sector Restricted Nonlinearities Research Articles

The H-infinity Control of a kind of Lurie Switched Time-delay System

The designation idea of infinity controller is introduced to a class of Lurie switched systems with time-delay and sector restricted nonlinearities. We Construct Lyapunov function and apply the stablity theory to analyze Lurie switched system. The theoretical proof showed that this system is gradually stable. The result is expressed by using linear matrix inequality (LMI), so it is easy to realize.

Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay

In this Letter, the synchronization problem for a class of complex dynamical networks in which every identical node is a Lur'e system with time-varying delay is considered. A delay-dependent synchronization criterion is derived for the synchronization of complex dynamical network that represented by Lur'e system with sector restricted nonlinearities. The derived criterion is a sufficient condition for absolute stability of error dynamics between the each nodes and the isolated node. Using a convex representation of the nonlinearity for error dynamics, the stability condition based on the discretized Lyapunov–Krasovskii functional is obtained via LMI formulation. The proposed delay-dependent synchronization criterion is less conservative than the existing ones. The effectiveness of our work is verified through numerical examples.

Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control

In this paper, the effects of time delay on chaotic master–slave synchronization scheme are considered. Using delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur’e system with sector-restricted nonlinearities. The derived criterion is a sufficient condition for absolute stability of error dynamics between the master and the slave system. Using a convex representation of the nonlinearity, the stability condition based on the Lyapunov–Krasovskii functional is obtained via LMI formulation. The proposed delay-dependent synchronization criterion is less conservative than the existing ones. The effectiveness of our work is verified through numerical examples.

On a Generalization of the Kalman-Yakubovich-Popov Lemma

The purpose of this note is to develop a generalization of the K-Y-P lemma and to apply this result to the absolute stability of single-variable Lur'e systems with sector-restricted nonlinearities.