The Hybrid Control And Periodically Intermittent Control Of Nonlinear Systems

Nonlinear systems have been extensively investigated in practical application, andattract many researchers'attention. In this paper, in order to ensure the stabilizationor synchronization of nonlinear systems, different controllers are designed. The maincontents in this paper can be summarized as follows:The first section is introduction, in which we present research background, purposeand significance of nonlinear system, hybrid control and periodically intermittent con-trol, respectively. And then the research status quo and results of hybrid control andperiodically intermittent control are given. The methods, investigated actuality and theoutcome of synchronization are also introduced. Finally the organization of this paper ispresented.In Section 2, the hybrid control and synchronization of nonlinear systems are dis-cussed. Some suffcient conditions ensuring the globally asymptotical stability and ex-ponential stability of nonlinear system are obtained by designing hybrid control, whichconsist of switch control and impulsive control, based on analysis techniques, respectively.And then, the asymptotical synchronization and exponential synchronization criteria ofnonlinear systems are also given by using similar research methods. Finally, some numer-ical examples and simulations are presented to show the feasibility and effectiveness ofthe proposed methods.The stabilization and synchronization of nonlinear system with constant delays un-der periodically intermittent control are discussed in section 3. By using the Lyaponovfunction and analysis methods, the suffcient conditions of globally exponential stabilityof nonlinear system are obtained and the exponential synchronization criteria are alsoderived. Finally, some numerical simulations are presented to verify the obtained results.The lag synchronization of nonlinear systems with constant time-delay and the syn-chronization of nonlinear systems with variable time-delays under periodically intermit- tent control was investigated in the section 4, respectively, and studied based on p-norm.Some sufficient conditions of lag synchronization of nonlinear system with constant delayand the synchronization of nonlinear systems with variable time-delays under periodicallyintermittent control are obtained, respectively. In this section, we also studied the syn-chronization of nonlinear system with variable time-delay under periodically intermittentcontrol. This is the first time to study the lag synchronization and synchronization ofnonlinear system under the periodically intermittent control based on p-norm, the resultsobtained in this section are new and useful verified through some numerical simulations.