Modern Lyapunov Tools

Abstract

This chapter deals with various kinds of nonsmooth Lyapunov functions that are introduced for addressing different stability concepts such as ISS and finite time stability among others. To add universality, the Lyapunov approach is revisited in the infinite-dimensional setting and the exposition focuses on a broad class of dynamic systems, evolving in a Hilbert space. Multiple, semi-global, finite time stable, homogeneous, input-to-state stable Lyapunov functionals are conceptually introduced side by side. The stability analysis, capturing both strict and non-strict Lyapunov functionals, is performed, particularly involving Krasovskii–LaSalle invariance principle.