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|Title||Model Order Reduction Using LMI|
In this thesis, the problem of Frobenius Hankel (F H) norm, H2 norm and H1 norm reduced order approximations will be investigated. The necessary and su–cient conditions for the existence of an approximate solution within a specifled error γ will be found, these conditions are given in terms of a set of linear matrix inequalities (LMI) and a matrix rank constraint for both continuous and discrete time multi input-multi output systems. The alternating projection algorithm (APA) and the cone complementarity algorithm (CCA) are used to solve the rank constraint problem and a comparison between both algorithms is presented. Numerical algorithms which use the cone complementary algorithm and alternating projection method are proposed and a method of flnding an initial starting point is suggested. Comparison between H2, H1 and F H norms model reduction using LMI0s techniques is discussed to show the efiectiveness of these methods. The proposed reduction method is extended to polytopic uncertain systems to show the efiectiveness of model order reduction using LMIs. Numerical examples are given to show and validate the effectiveness of the F H norm and H1 norm reduced order approximations using cone complementary algorithm to flnd at least as good approximates as other methods.
|Publisher||the islamic university|
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