Stability of non-polynomial systems using differential inclusions and polynomial Lyapunov functions

Abstract

The concept of linear differential inclusions is generalized to approximate a non polynomial system by polynomial systems. In parallel with the use of linear differential inclusions in the study of non-linear system stability, the right hand side of the non-linear system is expressed as a convex combination of the approximating polynomials. A common Lyapunov function for the approximating polynomials establishes the stability of the non-linear system. The common polynomial Lyapunov function can be calculated by using the recently developed sum of squares methods.