Study Of Stabilization And Synchronization With Special Nonlinear Systems

Lur'e system is a class of typical nonlinear system. During the past decades,synchronization of Lur'e systems has received considerable interest because this type ofsystems are widely applied in various fields of science and engineering. synchronization ofdynamical complex networks consisting of Lur'e systems and Lagrange stabilisation foruncertain phase-controlled systems have become a topic of great interest. The maincontributions of this dissertation are as follows:Firstly, A stabilization problem for dynamical complex networks of coupled by chaosLur'e systems is concerned with. By using some results of Popov theory and a specialdecentralized control strategy, we address the problem of designing a linear feedbackcontroller such that states of all nodes are globally stabilized onto an expected homogeneousstate. A network composed of identical Chua's circuits is adopted as a numerical example todemonstrate the effectiveness of the proposed results.Secondly, The Lagrange stabilization problem for uncertain phase-controlled systemswith parameter uncertainties is concerned with. By using the Kalman-Yakubovich-Popovlemma, linear matrix inequality (LMI) conditions for Lagrange stability of nominalphase-controlled systems are derived. The allowable uncertainty bounds for controllabilityand observability and time-domain conditions for Lagrange stability of uncertainphase-controlled systems are presented. A controller design strategy based on the LMImethod is proposed such that the uncertain phase-controlled systems are Lagrange stabilized.Synchronous single-phase motor with pulsing vibrating moment is provided to demonstratethe effectiveness of the proposed results.Finally, Synchronization of Lur'e systems with more restrictively slope restrictions onthe nonlinearities are studied by using time-delay feedback control. Choosing aLur'e-Postnikov function as Lyapunov-like function, novel and less conservativedelay-dependent synchronization criterion is presented by applying KYP lemma and Schurcomplement formula. Synchronization of a given system can be determined by solving a LMIfeasible problem and the maximum upper bound of allowable time delay can be obtained by solving an optimization problem. The given synchronization criterion and some existing onesare employed to Chua's circuit and Chua's oscillator to demonstrate the effectiveness of thegiven results.