Noncoercive Lyapunov Functions for Input-to-State Stability of Infinite-Dimensional Systems
Birgit Jacob, Andrii Mironchenko, J. R. Partington, Fabian Wirth
Abstract
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 (ISS). This property in turn is equivalent to ISS, if the system has some sort of regularity. 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.
Topics & Concepts
Lyapunov functionMathematicsStability (learning theory)State (computer science)Nonlinear systemSubject (documents)Control theory (sociology)Dynamical systems theoryApplied mathematicsMathematical economicsComputer scienceControl (management)Artificial intelligenceLibrary scienceAlgorithmPhysicsMachine learningQuantum mechanicsControl and Stability of Dynamical SystemsStability and Controllability of Differential EquationsStability and Control of Uncertain Systems