Abstract
systems, known as bounded real balanced truncation and positive real balanced
truncation respectively, is addressed. Results for finitedimensional systems were established
in the mid to late 1980s and we consider two extensions of this work. Firstly,
using a more behavioral framework we consider the notion of a finitedimensional dissipative
system, of which bounded real and positive real inputstateoutput systems are
particular instances. Specifically, we work in a framework where we make no a priori
distinction between inputs and outputs. We derive model reduction by dissipative balanced
truncation, where a gap metric error bound is obtained, and demonstrate that
the aforementioned bounded real and positive real balanced truncation can be seen as
special cases.
In the second part we generalise bounded real and positive real balanced truncation
to classes of bounded real and positive real systems respectively that have nonrational
transfer functions, so called infinitedimensional systems. Here we work in the context
of wellposed linear systems. We derive approximate transfer functions, which we
prove are rational and preserve the relevant dissipativity property. We also obtain error
bounds for the difference of the original transfer function and its reduced order transfer
function, in the Hinfinity norm and gap metric for the bounded real and positive real
cases respectively. This extension to bounded real and positive real balanced truncation
requires new results for Lyapunov balanced truncation in the infinite dimensional case,
which we also describe. We conclude by highlighting possible future research.
Language  English 

Qualification  Ph.D. 
Awarding Institution 

Supervisors/Advisors 

Award date  26 Jun 2012 
Status  Published  2012 
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Cite this
Model Reduction by Balanced Truncation. / Guiver, Christopher.
2012. 203 p.Research output: Thesis › Doctoral Thesis
}
TY  THES
T1  Model Reduction by Balanced Truncation
AU  Guiver,Christopher
PY  2012
Y1  2012
N2  Model reduction by balanced truncation for bounded real and positive real inputstateoutputsystems, known as bounded real balanced truncation and positive real balancedtruncation respectively, is addressed. Results for finitedimensional systems were establishedin the mid to late 1980s and we consider two extensions of this work. Firstly,using a more behavioral framework we consider the notion of a finitedimensional dissipativesystem, of which bounded real and positive real inputstateoutput systems areparticular instances. Specifically, we work in a framework where we make no a prioridistinction between inputs and outputs. We derive model reduction by dissipative balancedtruncation, where a gap metric error bound is obtained, and demonstrate thatthe aforementioned bounded real and positive real balanced truncation can be seen asspecial cases.In the second part we generalise bounded real and positive real balanced truncationto classes of bounded real and positive real systems respectively that have nonrationaltransfer functions, so called infinitedimensional systems. Here we work in the contextof wellposed linear systems. We derive approximate transfer functions, which weprove are rational and preserve the relevant dissipativity property. We also obtain errorbounds for the difference of the original transfer function and its reduced order transferfunction, in the Hinfinity norm and gap metric for the bounded real and positive realcases respectively. This extension to bounded real and positive real balanced truncationrequires new results for Lyapunov balanced truncation in the infinite dimensional case,which we also describe. We conclude by highlighting possible future research.
AB  Model reduction by balanced truncation for bounded real and positive real inputstateoutputsystems, known as bounded real balanced truncation and positive real balancedtruncation respectively, is addressed. Results for finitedimensional systems were establishedin the mid to late 1980s and we consider two extensions of this work. Firstly,using a more behavioral framework we consider the notion of a finitedimensional dissipativesystem, of which bounded real and positive real inputstateoutput systems areparticular instances. Specifically, we work in a framework where we make no a prioridistinction between inputs and outputs. We derive model reduction by dissipative balancedtruncation, where a gap metric error bound is obtained, and demonstrate thatthe aforementioned bounded real and positive real balanced truncation can be seen asspecial cases.In the second part we generalise bounded real and positive real balanced truncationto classes of bounded real and positive real systems respectively that have nonrationaltransfer functions, so called infinitedimensional systems. Here we work in the contextof wellposed linear systems. We derive approximate transfer functions, which weprove are rational and preserve the relevant dissipativity property. We also obtain errorbounds for the difference of the original transfer function and its reduced order transferfunction, in the Hinfinity norm and gap metric for the bounded real and positive realcases respectively. This extension to bounded real and positive real balanced truncationrequires new results for Lyapunov balanced truncation in the infinite dimensional case,which we also describe. We conclude by highlighting possible future research.
M3  Doctoral Thesis
ER 