Abstract
In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to the algorithms is a number of frequency response samples of the original model. This makes the computational complexity relatively low for largescale models. Extra properties on a reduced model can also be enforced, as long as the properties can be expressed as convex conditions. Semidefinite program are solved using the interior point methods which are well developed, making the implementation simpler.
A number of extensions to the proposed methods were studied, for example, passive model reduction, frequencyweighted model reduction. An interesting extension is reduction of parameterized linear time invariant models, i.e. models with statespace matrices dependent on parameters. It is assumed, that parameters do not depend on state variables nor time. This extension is valuable in modeling, when a set of parameters has to be chosen to fit the required specifications. A good illustration of such a problem is modeling of a spiral radio frequency inductor. The physical model depends nonlinearly on two parameters: wire width and wire separation. To chose optimally both parameters a loworder model is usually created. The inductor modeling is considered as a case study in this thesis.
A number of extensions to the proposed methods were studied, for example, passive model reduction, frequencyweighted model reduction. An interesting extension is reduction of parameterized linear time invariant models, i.e. models with statespace matrices dependent on parameters. It is assumed, that parameters do not depend on state variables nor time. This extension is valuable in modeling, when a set of parameters has to be chosen to fit the required specifications. A good illustration of such a problem is modeling of a spiral radio frequency inductor. The physical model depends nonlinearly on two parameters: wire width and wire separation. To chose optimally both parameters a loworder model is usually created. The inductor modeling is considered as a case study in this thesis.
Original language  English 

Qualification  Licentiate 
Awarding Institution 

Supervisors/Advisors 

Award date  2009 Nov 27 
Publisher  
Publication status  Published  2009 
Subject classification (UKÄ)
 Control Engineering
Keywords
 semidefinite programming
 model reduction
 convex optimization