Fourth-order Constant Coefficient Linear Systems, Lyapunov Function Construction And The Fourth Order Nonlinear System Stability

This paper is divided into three parts.The first part is concerned with the basic theory of the stability.The second part has studied the construction of Liapunos' function of thefourth-order linear systems and the last part has derived condition of the stability of the nonlinear systems.With the development of the society and the technology , the stability of the differential eqation has been widely used in many fields .But the key to studying the stability is to look for Liapunov's function .Many researchers have made Liapunov's function of the second and third-order linear systems. In this paper , we have turned the fourth - dimension linear system with contant coefficient into the different equivalence systems and figured out the Liapunov's functions .Since 1950's , the stability of differential eqation has been developed and drawn the researcher's attention. In this paper ,we have made up the Liapunov s functions of the fourth - order nonlinear systems by the use of " comparison method " and derived the sufficient conditions of the stability of the nonlinear system on base of the chapter 2.