Abstract
Abstract : An approach is proposed for the construction of Liapunov functions for certain types of second and third-order nonlinear systems. If the system is described by a vector differential equation, a Liapunov function which ensures stability of the linear system for all values is called a common Liapunov function (CLF) in the given range. While it may prove difficult to determine such a CLF, a Liapunov function may be selected to ensure the stability of the linear system over the entire range of the parameters. Under certain conditions, this Liapunov function may be easily modified for use as a Liapunov function for a nonlinear system in which there are functions of the state variables. Using this approach, sufficient conditions are determined for the stability of a differential equation in terms of the bounds on certain functions.
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