Input-to-state stability for classes of nonlinear PDEs: an operator-theoretic approach / vorgelegt von René Hosfeld. Wuppertal, [2025]
Inhalt
- Symbols
- Introduction
- Preliminaries
- Basic notation
- Orlicz spaces
- Young functions
- Young functions of class P
- The Orlicz space L
- The Orlicz space E
- Orlicz–Sobolev spaces
- Operator semigroups
- Linear systems theory
- Linear input systems
- Admissible control operators and mild solutions
- Testing admissibility of control operators
- Regularity of solutions
- Linear output systems
- Admissible observation operators and outputs
- Duality of admissible operators
- Testing admissibility of observation operators
- System nodes and well-posedness
- On the Weiss conjecture for Orlicz spaces
- Input-to-state stability
- Input-to-state stability of bilinear control systems
- Input-to-state stability of bilinear feedback systems
- Local input-to-state stability for bilinear feedback systems
- Global input-to-state stability for bilinear feedback systems
- Examples
- Input-to-state stability of a semilinear wave equation
- Bounded-input-bounded-output stability
- BIBO stability of semilinear state space systems
- Global Lipschitz nonlinearities
- Locally Lipschitz nonlinearities
- An application to funnel control
- Bibliography