Robustness of linear algebra properties for Port-Hamiltonian systems

Abstract: Port-Hamiltonian systems are an important class of control systems that arise in all areas of science and engineering. When the system is linearized around a stationary solution one gets a linear port-Hamiltonian system. Despite the fact that the system looks unstructured at first sight, it has remarkable properties. Stability and passivity are automatic, spectral structures for purely imaginary eigenvalues, eigenvalues at infinity, and even singular blocks in the Kronecker canonical form are very restricted and furthermore the structure leads to fast and efficient iterative solution methods for associated linear systems. When port-Hamiltonian systems are subject to (structured) perturbations, then it is important to determine the minimal allowed perturbations so that these properties are not preserved. The computation of these structured distances to instability, non-passivity, or non-regularity, is typically a very hard optimization problem. However, in the context of port-Hamiltonian systems, the computation becomes much easier and can even be implemented efficiently for large scale problems in combination with model reduction techniques. We will discuss these distances and the computational methods and illustrate the results via an industrial problem in the context of noise reduction for disk brakes.

numerical analysis

Audience: researchers in the topic

E-NLA - Online seminar series on numerical linear algebra

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