Stabilisation of infinite-dimensional port-Hamiltonian systems via dissipative boundary feedback / vorgelegt von Dipl.-Math. Björn Augner aus Hamburg. Wuppertal, [2016?]
Inhalt
- Introduction
- Some Background on Functional Analysis, Evolution Equations and Systems Theory
- Background on Functional Analysis and Partial Differential Equations
- Background on Evolution Equations
- Background on Systems Theory
- Hyperbolic Partial Differential Equations on a One-dimensional Spatial Domain
- Stabilisation of Port-Hamiltonian Systems via Static Linear Boundary Feedback
- Known Results for the Case N = 1
- Asymptotic Stability
- Uniform Exponential Stability
- First Order Port-Hamiltonian Systems
- Second Order Port-Hamiltonian Systems
- Euler-Bernoulli Beam Equations
- Arbitrary N N – The Full Dissipative Case
- On the H-dependence of stability properties
- Examples
- Passivity Based Dynamic Linear Feedback Stabilisation
- The Generation Theorem – Dynamic Case
- Asymptotic Behaviour
- Strictly Input Passive Controllers
- Strictly Output Passive Controllers
- More General Impedance Passive Controllers
- The Static and the Dynamic Case
- Examples
- Nonlinear Boundary Feedback: the Static Case
- The Generation Theorem – Static, Nonlinear Case
- Exponential Stability: the Case N = 1
- Stabilisation: the Case N > 1
- Stabilisation of the Euler-Bernoulli Beam
- Examples
- Passivity Based Nonlinear Dynamic Feedback Stabilisation
- m-Dissipative Dynamic Control Systems
- An Alternative Approach
- The Nonlinear Control System
- Local Existence of Solutions
- Interconnection of Impedance Passive Systems
- Exponential Stability
- Further Results
- Interconnection of Infinite Dimensional Port-Hamiltonian Systems
- Non-autonomous Systems: The Case N = 1
- Systems with Structural Damping
- Bibliography