Stability regions of nonlinear dynamical systems: a constructive methodology

A constructive methodology for estimating stability regions of general nonlinear dynamical systems is developed. The constructive methodology starts with a given Lyapunov function (either a global or a local Lyapunov function) and yields a sequence of Lyapunov functions which are then used to estimate the stability region. The resulting sequence of estimated stability regions is shown to be a strictly monotonic increasing sequence, and yet each of them remains inside the entire stability region. The significance of this methodology includes: its ability to reduce significantly the conservativeness in estimating the stability regions; its computational efficiency; its adaptability; and its sound theoretical basis