Estimation of asymptotic stability regions via homogeneous polynomial Lyapunov functions

Asymptotic stability regions of nonlinear dynamical systems are estimated by using homogeneous polynomial Lyapunov functions, which include quadratic Lyapunov functions as a special case. The nonlinear system is represented as a convex hull of some linear systems, and it is shown that the estimation can be formulated as an LMI optimization problem in an augmented state space.