An Extended Lyapunov-Density Condition for Nonlinear Time-Varying Systems

Lyapunov densities have been receiving a considerable amount of attention in the last two decades as a method of stability analysis. This paper extends the recently presented Lyapunov density conditions for nonlinear time-varying systems with introducing additional freedom in the inequalities on Lyapunov densities. Then the proposed inequality condition with the additional freedom leads to a convex formulation of robustly stabilizing state-feedback synthesis of nonlinear systems that have time-varying uncertainties. A numerical example demonstrates the usefulness of the proposed inequalities for the robust stabilization problem.