A Smooth Converse Lyapunov Theorem for Robust Stability

. This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets. 1. Introduction. This work is motivated by problems of robust nonlinear stabilization. One of our main contributions is to provide a statement and proof of a Converse Lyapunov Function Theorem which is in a form particularly useful for the study of such feedback control analysis and design problems. We provide a single (and natural) unified result that: 1. applies to stability with respect to not necessarily compact invariant sets; 2. deals with global (as opposed to merely loca...