Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 58, Issue 5, Pages 2952-2978Publisher
SIAM PUBLICATIONS
DOI: 10.1137/19M1297506
Keywords
infinite-dimensional systems; input-to-state stability; Lyapunov functions; nonlinear systems; linear systems
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Funding
- German Research Foundation (DFG) [MI 1886/2-1]
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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.
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