Infinite-dimensional port-Hamiltonian systems with a stationary interface

2023/01/21 by Alexander Kilian, Bernhard Maschke, Kilian, Alexander +5
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Control and Stability of Dynamical Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.08967

Abstract

We consider two systems of two conservation laws that are defined on complementary, one-dimensional spatial intervals and coupled by an interface as a single port-Hamiltonian system. In case of a fixed interface position, we characterize the boundary and interface conditions for which the associated port-Hamiltonian operator generates a contraction semigroup. Furthermore, we present sufficient conditions for the exponential stability of the generated C₀-semigroup. The results are illustrated by the example of two acoustic waveguides coupled by a membrane interface.

Related

• Infinite-Dimensional Port-Hamiltonian Systems with a Moving Interface
• A case study of port-Hamiltonian systems with a moving interface
• Asymptotic Stability of port-Hamiltonian Systems
• Stability via closure relations with applications to dissipative and port-Hamiltonian systems
• Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain: An Introduction