Abstract
The stability of nonlinear differential equations has been widely studied based on various methods. In this paper, we transform a class of fourth-order differential equations into a perturbation system and study the stability and asymptotic stability of zero solutions. By utilizing Lyapunov’s second method, we give sufficient conditions for zero-solution stability and asymptotic stability and provide the construction method of the zero-solution asymptotically stable Lyapunov function of such fourth-order differential equations. In addition, this paper removes the requirement of negative definite when the general differential equation is zero solution stable and obtains a looser stability condition. This paper provides an alternative approach to the research of stability of differential systems.
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