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| Author(s): |
Gustavo Sales Mazzoccante
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação |
| Defense date: | 2017-10-27 |
| Examining board members: |
Ricardo Coração de Leão Fontoura de Oliveira;
Daniel Dotta;
Eduardo Nunes Gonçalves
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| Advisor: | Ricardo Coração de Leão Fontoura de Oliveira |
| Abstract | |
This dissertation deals with the model reduction problem for uncertain linear continuous- and discrete-time systems, allowing the reduction of the number of states as well as the removal of uncertain parameters. The system matrices to be reduced are described in terms of time invariant parameters with polynomial dependency of arbitrary degree, with additive norm-bounded terms. The H-2 and H-infinity norms associated to the dynamics of the approximation error between the original and reduced systems are used as performance criteria of the reduction procedure. The proposed synthesis conditions are expressed in terms of parameter-dependent linear matrix inequalities, which can be solved by relaxtion techniques that consider the optimization variables as fixed-degree polynomials. A convenient choice for the degrees of the variables used to construct the reduced system matrices provides total control over the parametric dependence of the resulting reduced system matrices. The main usage of this possibility is the removal of uncertain parameters from the model. This flexibility is a novelty in the model reduction literature. In addition, the problem of model reduction using the H-infinity norm with low frequency specification is approached using an extension of the Kalman-Yakubovich-Popov Lemma, providing synthesis conditions for uncertain systems in continuous-time more suitable from a practical point of view. Scalar searches and iterative procedures are proposed as auxiliary strategies to reduce the conservatism of the presented conditions. Numerical examples borrowed from the literature illustrate the advantages of the technique when compared to the existing methods (AU) | |
| FAPESP's process: | 15/16600-2 - Order reduction of uncertain models by means of LMI relaxations with scalar searches |
| Grantee: | Gustavo Sales Mazzoccante |
| Support Opportunities: | Scholarships in Brazil - Master |