The main contribution of this dissertation is to propose conditions for linear filter and controller design, considering both robust and parameter dependent structures, for discrete time-varying systems. The controllers, or filters, are obtained through the solution of optimization problems, formulated in terms of bilinear matrix inequalities, using a method that alternates convex optimization problems described in terms of linear matrix inequalities. Both affine and multi-affine in different instants of time (path dependent) Lyapunov functions were used to obtain the design conditions, as well as extra variables introduced by the Finsler's lemma. Design problems that take into account an H-infinity guaranteed cost were investigated, providing robustness with respect to unstructured uncertainties. Numerical simulations show the efficiency of the proposed methods in terms of H-infinity performance when compared with other strategies from the literature.
Electric filters, Digital--Computer simulation., Linear control systems--Computer simulation., Lyapunov functions.
FundaÃ§\xe3o de Amparo Ã Pesquisa do Estado de S\xe3o Paulo (State of Sao Paulo Research Foundation); CoordenaÃ§\xe3o de AperfeiÃ§oamento de Pessoal de Nível Superior (Coordination of Improvement of Higher Education); Electrical and Computer Department of the University of New Mexico.
Level of Degree
Electrical and Computer Engineering
Abdallah, Chaouki Tanios
First Committee Member (Chair)
Heileman, Gregory L.
Second Committee Member
Third Committee Member
do Val, Joao Bosco Ribeiro
Fourth Committee Member
Peres, Pedro Luis Dias
Borges, Renato Alves. "Control and filtering of time-varying linear systems via parameter dependent Lyapunov functions." (2009). http://digitalrepository.unm.edu/ece_etds/38