Stability With Respect To Partial Variables Of A Class Of Time-Varying Systems And Its Applications In Chaos Synchronization

This thesis is devoted to the investigation of stability with respect to partial variables of a class of time-varying systems and its applications in chaos synchronization. After a brief description of historical background and research progress in this field, the research work of this paper focus on the two aspects:1) Theoretical Results. Based on the Lagrange formula with constants variables, some new sufficient conditions for ensuring globally exponential stability of such systems are derived. The results include and improve some results associated with the same problems in the literature.2) Applications. The above theoretical results are applied to control chaos synchronization of some well-known chaotic systems as follows: (1).Feedback and adaptive synchronization of Lu system. (2). Higher-order antithetical couplets synchronization of gravity wave equation with the primary soud. (3). Robust synchronization of Lorenz system. Furthermore, numerical simulations also demonstrate the effectiveness of the proposed control techniques.It is believed that the results of this paper should provide some important guidance for this kind of engineering design and applications.