COMPUTER-GENERATION OF LYAPUNOV FUNCTIONS AND ESTIMATION OF A STABILITY REGION

The Lyapunov method is one of the most powerful methods for analysis o f stability. However, from the practical viewpoint, there is no method to construct a Lyapunov function applicable to systems in general. Th is paper presents the Lyapunov function that is determined by a polyto pe and which is suitable for computer generation of Lyapunov functions since neither a special form of function nor the number of parameters to be chosen need be given in advance. Moreover, the estimate of the stability region can easily be improved since the modification of Lyap unov function is that of the corresponding polytope. In this paper, th e notion of the traditional sector condition is generalized so that a given function is bounded by using the convex combination of a set of piecewise-linear functions. Using this generalized sector condition, i mproved stability conditions are derived and it is applied to construc t the Lyapunov function.