AN EXTENDED INTEGRAL METHOD TO DERIVE LYAPUNOV FUNCTIONS FOR NONLINEAR-SYSTEMS

In this paper, Chin's (1987 b) integral method of deriving Lyapunov fu nctions for the investigation of nonlinear system stability is extende d. Whereas in Chin's method, each weighting function includes only one state variable, in the extended integral method the weighting functio ns can be any continuous functions of time, some or all state variable s and their time derivatives. As a result of the less restrictive weig hting functions, the sensitivity of the method to the form of the stat e-space model is reduced, which gives the user more freedom in derivin g the Lyapunov functions. The method also extends the integral method in the sense that it can be applied to both autonomous and non-autonom ous systems. Furthermore, the intrinsic method of Chin (1988) is shown to be a special case of the extended integral method. Many examples f rom the literature and from engineering applications are provided to s how that the extended method is surprisingly easy to apply, and result s in Lyapunov functions for more general systems.