An Algebraic Approach on Globally Exponential Stability of Polynomial Dynamical Systems

This paper presents a constructive method for analyzing globally exponential stability of polynomial dynamical systems by discovering quadratic Lyapunov functions. First, we derive an algebraic sufficient condition for analyzing globally exponential stability. Then, we apply a real root classification (RRC) based method step by step to under-approximate this derived condition as a semi-algebraic set which only involves the parametric coefficients of the candidate polynomials and the parameter associated with the exponential decay rate. Finally, we compute a sample point in the resulting semi algebraic set for the parameters resulting in a Lyapunov function and an exponential decay rate. The experimental results and comparisons demonstrate the feasibility and promise of our approach.