The Stability Of Lurie System And Its Applications In Chaos Synchronization

This paper considers the problem of absolute stability of time-delay Lurie control systems and its applications in chaotic synchronization. The main purpose is to derive the delay-dependent absolute stability conditions for the time-delay Lurie control systems and its application in Master-Slave synchronization of Lurie chaotic systems, which including the following content:1. Based on constructing Lyapunov functions and decomposing the coefficient of the time-delay item, some delay-dependent absolute stability criteria for multiple times-delay Lurie system are derived. The criterion is given in the form of linear matrix inequality (LMI). According to adding slack matrices and using the descriptor system approach, a larger delay bound ensuring the system absolute stability is obtained by solving a convex optimization problem of the linear matrix inequality. The numerical example given in this paper demonstrates our results.2. The robust stability of uncertain Lurie control systems with time-delays is investigated. Using the method mentioned in the second chapter, a delay-dependent robust stability condition is derived for the uncertain Lurie systems with structure uncertainty.3. A general method dealing with the synchronization of a class of Master-Slave chaotic Lurie system is introduced by constructing error systems. Using the method mentioned above, a novel synchronization condition is gained and a larger bound for the absolute stability of the error system is obtained. The numerical example demonstrates that our results are less conservative than the existed results.Above all, the absolute stability problem of multiple time-delays Lurie system is considered in this paper and two different delay-dependent conditions are derived. Based on this, the robust absolute stability criterion of uncertain time-delay Lurie system is researched and the method to process the Lurie master-slave synchronization is introduced.