Lyapunov function computation for nonlinear systems through dynamical embedding – A case study

We present the computational stability analysis and the domain of attraction estimation of a non-polynomial system using dynamical embedding. The Lyapunov function is searched in a general quadratic form of rational terms in the embedding state space. To ensure that the Lyapunov conditions are satisfied, sufficient polytopic linear matrix inequalities are formulated using Finsler’s lemma and affine annihilators. A compact forward invariant region is finally given as an appropriate level set of the Lyapunov function in the original system of coordinates. The concepts are demonstrated through a dynamically extended rational fourth-order model of the one degree-of-freedom inverted pendulum system.