When Do Lyapunov Functions Exist on Invariant Neighborhoods

摘要: Publisher Summary This chapter discusses the existence of Lyapunov functions on invariant neighborhoods. The theory characterization via compact asymptotically stable sets dynamical systems defined locally metric spaces is essentially complete. Krasovskii extended such critical points differential to include more general situation where a point has neighborhood containing no other complete trajectories. Further notable developments in these directions have been obtained, for example, autonomous and spaces. In contrast sets, characterizing are generally not available any neighborhoods an isolated set. results tubes ∞-tubes as noncritical that form basis parallelizable systems.