Optimal robustness of port-Hamiltonian systems
For control theorists and engineers, this provides a method to ensure robustness in port-Hamiltonian systems, though the solution for non-passive systems is suboptimal.
The paper constructs optimally robust port-Hamiltonian realizations for passive systems, showing that the realization with maximal passivity radius is normalized and providing an algorithm for its computation. It also addresses finding the nearest passive system to a non-passive one with a suboptimal solution.
We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to construct this optimal solution. We also consider the problem of finding the nearest passive system to a given non-passive one and provide a simple but suboptimal solution.