ON THE STABILITY DOMAIN ESTIMATION VIA A QUADRATIC LYAPUNOV FUNCTION - CONVEXITY AND OPTIMALITY PROPERTIES FOR POLYNOMIAL SYSTEMS

The problem of estimating the stability domain of the origin of an n-o rder polynomial system is considered. Exploiting the structure of this class of systems it is shown that, for a given quadratic Lyapunov fun ction, an estimate of the stability domain can be obtained by solving a suitable convex optimization problem. This estimate is shown to be o ptimal for an important subclass including both quadratic and cubic sy stems, and its accuracy in the general polynomial case is discussed vi a several examples.