An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
Stability and Stabilization of Infinite Dimensional Systems with Applications
Stability and Stabilization of Infinite Dimensional Systems with Applications
L2-Gain and Passivity Techniques in Nonlinear Control
L2-Gain and Passivity Techniques in Nonlinear Control
Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators
SIAM Journal on Control and Optimization
Mathematical modeling for nonlinear control: a Hamiltonian approach
Mathematics and Computers in Simulation
Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity
Automatica (Journal of IFAC)
Hamiltonian discretization of boundary control systems
Automatica (Journal of IFAC)
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This contribution presents two approximation methods for linear infinite-dimensional systems that ensure the preservation of stability and passivity. The first approach allows one to approximate internal source free infinite-dimensional systems such that the resulting approximation is a port-controlled Hamiltonian system with dissipation. The second method deals with the class of systems that are not required to have conjugated outputs but only a dissipative system operator. It yields approximations with a dissipative system matrix for which bounds of their stability margin are provided. Both approaches are based on a state space formulation of the infinite-dimensional system. This makes it possible to use the Petrov-Galerkin approximation whose free parameters are partly used for achieving the structure preservation. Since still free parameters remain, further application specific objectives, such as, e.g., moment matching, can be achieved. Both approaches are applied to the approximation of an Euler-Bernoulli beam.