Robust synthesis for master-slave synchronization of Lur'e systems

Abstract

Abstract-In this paper a method for robust synthesis of full static-state error feedback and dynamic-output error feedback for master-slave synchronization of Lur'e systems is presented. Parameter mismatch between the systems is considered in the synchronization schemes. Sufficient conditions for uniform synchronization with a bound on the synchronization error are derived, based on a quadratic Lyapunov function. The matrix inequalities from the case without parameter mismatch between the Lur'e systems remain preserved, but an additional robustness criterion must be taken into account. The robustness criterion is based on an uncertainty relation between the synchronization error bound and the parameter mismatch. The robust synthesis method is illustrated on Chua's circuit with the double scroll. One observes that it is possible to synchronize the master-slave systems up to a relatively small error bound, even in the case of different qualitative behavior between the master and the uncontrolled slave system, such as limit cycles and stable equilibria.

Development of a Fractional Order Chaos Synchronization Dynamic Error Detector for Maximum Power Point Tracking of Photovoltaic Power Systems

“…The chaos system makes dramatic change in micro variation. The chaos synchronization synchronizes the kinematic trajectories of two chaos systems, and the controller makes the error zero [18,19]. In the chaos synchronization system, the two chaos systems are called Master System (MS) and Slave System (SS).…”

Decentralised static output feedback stabilisation and synchronisation of networks

“…The solution to (28)- (29) provides the s(t) to which the states of the network are to be synchronised to. To develop a controller to induce synchronicity, as in [3,7,25], define an error vector e i (t) := x i (t) − s(t) for i = 1 . .…”

“…To demonstrate the theory developed in this paper, a network of Chua oscillators [25] will be utilized. Consider an arbitrary graph G representing a network of dynamical systems consisting of 75 nodes.…”

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New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

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