Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems

In this note, we derive conditions of existence of a homogeneous polynomial Lyapunov function of an arbitrary even degree establishing global asymptotic stability of linear system with box-bounded uncertainty. Verification of these conditions is reduced to solving a convex minimization problem. We produce numerical examples that demonstrate significant improvement in estimates of admissible uncertainty bounds compared with estimates obtained via the most commonly used quadratic Lyapunov functions