COMPUTER-GENERATED LYAPUNOV FUNCTIONS FOR A CLASS OF NONLINEAR-SYSTEMS

In this paper, the problem of constructing Lyapunov functions for a cl ass of nonlinear dynamical systems is considered. The problem of const ructing a Lyapunov function is reduced to the construction of a polyto pe satisfying some conditions. A generalization of the concept of sect or condition is proposed so that it makes possible to evaluate a given nonlinear function by using a set of piecewise-linear functions. This improvement reduces the conservatism in the stability analysis of non linear systems very much. Two algorithms to construct such polytopes a re proposed, and two examples are shown to demonstrate the usefulness of the obtained results.