2019/11/04 by Birgit Jacob, Jacob, B., Andrii Mironchenko +5
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1911.01327
openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this class, the significance of noncoercive Lyapunov functions is analyzed. It is shown that the existence of such Lyapunov functions implies norm-to-integral input-to-state stability. This property in turn is equivalent to input-to-state stability, if the system satisfies certain mild regularity assumptions. For a particular class of linear systems with unbounded admissible input operators, explicit constructions of noncoercive Lyapunov functions are provided. The theory is applied to a heat equation with Dirichlet boundary conditions.