Studies On The Stabilization Of A Class Of Nonlinear Systems

The stability of control system is an important ingredient of system analysis. Stabilization of a system is the precondition for control system to work well. For a real control system, the stability is a most important property, so it is necessary to design control method to make the system stability. The key basis to analyze the stability of system is the Lyapunov's stability theory.There have been much more achievements on the Chua's circuit such as the follow control method, the exoganic feedback control method et al.. Distinguished from the above mentioned, the Small Gain theorem is employed in the paper to stabilize the Chua Circuit. The controlling method based on the Small Gain theorem is the linear feedback control, and the control designed on the Small Gain theorem can keep controlled system global stability at the balance point quickly. This control method is to divide the high dimensional system into several low dimensional systems, and then to design the linear feedback control for subsystems, and make them meet the condition of the Small Gain theorem. The method is to control the high dimensional chaos system through controlling the low dimensional systems so as to keep the controlled system global stability at the any balance point.Furthermore,the issue of ecology has been recognized gradually. Biological system is the nonlinear system, so it is still a public problem upon how to control the biological system balance. The predecessor has done a lot of researches. Taking the prey-preyed biological system as an example, the control strategy was designed by using properties of the Casecade system. And the system was stabilized at the normal balance point. The result could be used as theoretical basis to keep ecological system balance.