Abstract
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 bounded real singular values. By using the Cayley transform a gap metric error bound for positive real balanced truncation is subsequently obtained. For a class of systems with an analytic semigroup, we show rapid decay of the bounded real and positive real singular values. Together with the established error bounds, this proves rapid convergence of the bounded real and positive real balanced truncations.
Highlights
In model reduction the aim is to approximate a system with many degrees of freedom by a system with few degrees of freedom
In this article we are interested in the case where the original system has infinitely many degrees of freedom. Examples of such systems are systems described by partial differential equations or delay differential equations
We note that this reduced order transfer function is uniquely determined by the original transfer function, i.e., it does not depend on the particular bounded real balanced realisation that is chosen for truncation
Summary
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