Outputs (2)

Error bounds in the gap metric for dissipative balanced approximations (2013)
Journal Article
Guiver, C., & Opmeer, M. R. (2013). Error bounds in the gap metric for dissipative balanced approximations. Linear Algebra and its Applications, 439(12), 3659-3698. https://doi.org/10.1016/j.laa.2013.09.032

We derive an error bound in the gap metric for positive real balanced truncation and positive real singular perturbation approximation. We prove these results by working in the context of dissipative driving-variable systems, as in behavioral and sta... Read More about Error bounds in the gap metric for dissipative balanced approximations.

Bounded real and positive real balanced truncation for infinite-dimensional systems (2013)
Journal Article
Guiver, C., & Opmeer, M. R. (2013). Bounded real and positive real balanced truncation for infinite-dimensional systems. Mathematical Control and Related Fields, 3(1), 83-119. https://doi.org/10.3934/mcrf.2013.3.83

Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional case in terms of the bo... Read More about Bounded real and positive real balanced truncation for infinite-dimensional systems.