QUASI-STABILITY REGIONS OF NONLINEAR DYNAMICAL-SYSTEMS - THEORY

The concept of a stability region (region of attraction) of nonlinear dynamical systems is widely accepted in many fields such as engineerin g and the sciences, When utilizing this concept, the Lyapunov function approach has been found to give rather conservative estimations of th e stability regions of many nonlinear systems, In this paper we study the notion of a quasistability region and develop a comprehensive theo ry for it, It is shown that, working on the concept of quasi-stability regions, one can greatly overcome the problem of conservative estimat ions of stability regions using the Lyapunov function approach, A comp lete characterization of quasi-stability regions is presented, Dynamic al as well as topological properties of quasi-stability regions are al so derived, The quasi-stability regions are shown to be robust relativ e to small perturbations of the underlying vector fields, The class of nonlinear dynamical systems whose stability regions equal their quasi -stability regions is characterized.