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Model reduction by balanced truncation for systems with nuclear Hankel operators (2014)
Journal Article
Guiver, C., & Opmeer, M. R. (2014). Model reduction by balanced truncation for systems with nuclear Hankel operators. SIAM Journal on Control and Optimization, 52(2), 1366-1401. https://doi.org/10.1137/110846981

We prove the H-infinity error bounds for Lyapunov balanced truncation and for optimal Hankel norm approximation under the assumption that the Hankel operator is nuclear. This is an improvement of the result from Glover, Curtain, and Partington [SIAM... Read More about Model reduction by balanced truncation for systems with nuclear Hankel operators.

Positive state controllability of positive linear systems (2014)
Journal Article
Guiver, C., Hodgson, D., & Townley, S. (2014). Positive state controllability of positive linear systems. Systems and Control Letters, 65, 23-29. https://doi.org/10.1016/j.sysconle.2013.12.002

Controllability of positive systems by positive inputs arises naturally in applications where both external and internal variables must remain positive for all time. In many applications, particularly in population biology, the need for positive inpu... Read More about Positive state controllability of positive linear systems.

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.

A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds” (2011)
Journal Article
Guiver, C., & Opmeer, M. R. (2011). A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds”. IEEE Transactions on Circuits and Systems I: Regular Papers, 58(6), 1410-1411. https://doi.org/10.1109/tcsi.2010.2

We provide a counter example to the H∞ error bound for the difference of a positive real transfer function and its positive real balanced truncation stated in “Positive realness preserving model reduction with H-\infty norm error bounds” IEEE Trans.... Read More about A counter-example to “Positive realness preserving model reduction with H-\infty norm error bounds”.