Research On Stability Of Nonlinear Systems And Synchronization Control

Nonlinear system has broad application background in national defense, industry,human society and biosphere, and so on. And it has always been the hot topic of researchin the control feld. This dissertation mainly studies the stability and synchronizationcontrol problems of the nonlinear systems. The main works of this dissertation can besummarized into the following aspects:1. For the Lurie systems with time-varying delay, a delay decomposition method isemployed to solve the problems of robust absolute stability of direct system and neutralindirect system, respectively. By selecting suitable Lyapunov functions and diferent delaydivision methods, some delay-dependent conditions for absolute stability of these systemsare given. Through simulations and comparison, it can be found that the obtained resultsof this paper has less conservativeness.2. For the chaotic Lurie systems with sector and slope restricted nonlinearities,contraction analysis is used for the frst time to study the synchronization problem ofLurie systems with feedback controller. Without considering the stability of the errorsystem, synchronization condition for general Lurie systems is given. Furthermore, theresult is extended to the Chua's system whose nonlinear function is not diferentiable.Meanwhile, numerical simulations are also demonstrated to show the correctness of thetheoretical results.3. For Lurie complex dynamical networks, contraction analysis is utilized for thefrst time to study two synchronization problems of complex networks with diferentdelay-couplings. Based on contraction theory and matrix measure properties, the syn-chronization problem of system with constant coupling is frstly discussed, and then thesynchronization problem of system with constant coupling and discrete-delay coupling isalso considered. Some delay-independent synchronization conditions are proposed. Andsimulation results are illustrated to show the efectiveness of these conclusions.4. For the second-order multi-agent system with time-varying delay, the consen-sus problem of this system is studied. It is pointed out that the consensus problemof the second-order multi-agent system can be changed into the stability of the errorsystem about the linear multi-agent system. Then, the maximal advisable time-delaybound about the system achieving consensus is obtained through time-delay decomposi-tion method. The obtained results are presented in the form of linear matrix inequalities.This can help us to get a solution.5. For the second-order multi-agent systems with coupling strengths, the necessaryand sufcient conditions of these systems reaching leaderless consensus are frstly given by using some conclusions originated from the linear multi-agent systems. Then, the resultsare extended to the leader-following case. Numerical simulations are also given.6. For the multi-agent systems with general linear and nonlinear dynamics, con-traction analysis is used to consider their consensus problems for the frst time. Someconditions about these systems reaching consensus in leaderless and leader-following caseare presented. Moreover, simulation results are also given to validate the efectiveness ofthe conclusions.