Design Of State Feedback Controller And Observer For Chaotic Time-delay Systems

Owing to the appealing properties of chaotic system like unpredictability,strange attractors and sensitivity to initial conditions,chaos synchronization has flourished as an appealing research area in various applications,such as image encryption,communication security,biomedical engineering,chemical reaction and so on.In the field of biomedicine,the treatment of coronary artery related diseases is selected as the breakthrough point,and it is theoretically studied by the angle of chaotic synchronization control.Coronary artery is a kind of myocardial blood vessel and its main function is to transport nutrients and oxygen to the heart.Once obstruction and spasm occur,it will lead to angina pectoris,myocardial infarction and other diseases.In view of the synchronization of the coronary artery chaotic system,the paper mainly carries out the two aspects as follows:On the one hand,in the case of unmeasurable state and external uncertainty,the observer-based H_? synchronization control for coronary artery time-delay system is studied.By designing a Luenberger-like state observer,the state reconstruction of the healthy coronary artery system is realized,and the state reconstruction system is synchronized with the lesion system under the action of the controller.Based on the Lyapunov stability theory,by constructing suitable Lyapunov-Krasovskii functional,the observer-based synchronization control condition is derived for coronary artery system.Then,a decoupling method is designed to get the solution conditions of the separated observer and controller.On other hand,under the consideration of the input saturation limit,the synlchronizalion of uncertain coronary artery chaos systems with the input aind state tinme-varying delays is investigatced.Based oin Lyapunov stability theory and local sector condition,constructing an appropriate Lyapunov-Krasovskii functional,the controller design conditions based oin are derived for local synchronization of coronary artery chaos system.Meanwhile,considering the influence of external uncertainty to the system,a robust synchronous saturation control condition is derived.The above two aspects aim at the syinchronization problm of Lipschitz nonlinear chaotic system,but the research is extciiended to the synchronization control of the one-side Lipschitz nonlinear chaotic system in the following section.Compared with the traditionial Lipschiz conditions,one-sidced Lipschitz conditions have smaller conservativencss and wider application range.Considering one-sided Lipschitz nonlinearity and the external uncertainty,the H_? synchronization control for time-delay chaotic systems is studied.Based on the one-sided Lipschitz condition,quadratic inner boundedness and Lyapunov stability theory,the condition for robust synchronization control of chaotic systems is derived by constructing suitable Lyapunov-Krasovskii functional.