The Nonlinear System Of The Lyapunov Function Struccure And The Stability Analysis

This paper studies two aspects, First, the Lyapunov function construction bylinear system of the nonlinear system, Lyapunov function construction on this basis,the trivial solution stability of a few class of fourth order nonlinear systems, sufficientconditions of asymptotic stability; Second, the use of the Gronwall-BellmanInequality on n-dimensional nonlinear system ordinary solution stable, asymptoticallystable, consistent stable sufficient conditions were studied.The full text is divided into four parts:Part I: Introduction and lemma, the following discussion made the necessarypreparations;Part II: Discussed by Barbashin formula a constant coefficient linear differential equationsx⁴+ax^m+bxⁿ+cx’+dx=0various forms of Lyapunov function;Part III: Use of the Gronwall-Bellman inequality, and made appropriateimprovements to the restrictions of the Lyapunov function, The trivial solution ofn-dimensional nonlinear system stability theorem was obtaind;Part IV: Using the analogy of several types of fourth order nonlinear system,Lyapunov function construction, Sufficient conditions are given and discussed on thebasis of the nontrivial solution stability, asymptotically stable.