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Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems

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1 Author(s)
Zelentsovsky, A.L. ; Inst. for Syst. Studies, Moscow, Russia

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

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Automatic Control, IEEE Transactions on  (Volume:39 ,  Issue: 1 )