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I. H. da Cunha
Programa de Pós-Graduação em Engenharia Elétrica (PPGEL) do CEFET-MG/UFSJ, Av. Amazonas, 7675, Belo Horizonte, MG
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C. P. Castro
Departamento de Engenharia Mechatronica, CEFET–MG, Álvares Azevedo, 400, 35503-822, Divinópolis, MG
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L. F. P. Silva
Programa de Pós-Graduação em Engenharia Elétrica (PPGEL) do CEFET-MG/UFSJ, Av. Amazonas, 7675, Belo Horizonte, MG; Departamento de Engenharia Mechatronica, CEFET–MG, Álvares Azevedo, 400, 35503-822, Divinópolis, MG
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V. J. S. Leite
Programa de Pós-Graduação em Engenharia Elétrica (PPGEL) do CEFET-MG/UFSJ, Av. Amazonas, 7675, Belo Horizonte, MG; Departamento de Engenharia Mechatronica, CEFET–MG, Álvares Azevedo, 400, 35503-822, Divinópolis, MG
Keywords:
Discrete-time systems, partially matched premises, LMIs, Lyapunov function
Abstract
This work proposes a relaxation that results in better stability analysis and controller synthesis for discrete-time Takagi-Sugeno (T-S) fuzzy systems subject to partially matched assumptions. This case, in which the controller and system have the same number of rules but differ in the parameters, is a frequent case in control applications, which has a great practical interest. The proposed approach is based on representing the error between two membership functions (MFs) through a second-order polynomial. The conditions are proposed as convex optimization procedures formulated as linear matrix inequalities (LMIs), guaranteeing efficient numerical solutions. Two examples illustrate the proposal; where the first one compares the proposed analysis condition with one found in the literature. The second example uses the synthesis condition to guarantee the stability of the closed-loop system, and the T-S fuzzy controller has membership functions different from the T-S fuzzy system. The results achieved suggest the superiority of the proposed method.