A descriptor system approach to estimating domain of attraction for non-polynomial systems via LMI optimizations

A computational methodology of estimating the domain of attraction (DA) is addressed for non-polynomial systems by a descriptor system approach. For an existing technique of approximating a non-polynomial function, a further investigation is conducted on the existence of upper and lower polynomial bounds of the non-polynomial function. In formulation of the DA analysis conditions, an implicit form and a generalized Lyapunov function are utilized for dealing with the non-polynomial systems in polynomial fashion and provide two stability conditions which can be reduced to linear matrix inequality (LMI) problems. A relation between these conditions is also discussed. Numerical examples illustrate our DA analysis method.