QUASI-STABILITY REGIONS OF NONLINEAR DYNAMICAL-SYSTEMS - OPTIMAL ESTIMATIONS

In this paper, we develop an effective scheme to estimate stability re gions by using an energy function that is a generalization of the Lyap unov functions, It is shown that the scheme can optimally estimate sta bility regions, A fairly comprehensive study for the structure of the constant energy surface lying inside the quasi-stability region is pre sented. A topological characterization, as well as a dynamical charact erization for the point on the quasi-stability boundary and the point on the stability boundary with the minimum value of an energy function are derived, These characterizations are then used in the development of a computational scheme to estimate quasi-stability regions. By uti lizing an energy function approach (or Lyapunov function approach), th is scheme can significantly reduce conservativeness in estimating the stability region, because the estimated stability region characterized by the corresponding energy function is the largest one within that s tability region.