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# Controller and filtering design for fuzzy systems and hybrid systems through LMIs: Applications and extensions

 Grant number: 17/01771-1 Support Opportunities: Scholarships in Brazil - Post-Doctorate Effective date (Start): August 01, 2017 Effective date (End): May 20, 2018 Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls Acordo de Cooperação: Coordination of Improvement of Higher Education Personnel (CAPES) Principal Investigator: Pedro Luis Dias Peres Grantee: Luciano Antonio Frezzatto Santos Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil Abstract The study of stability analysis and the synthesis of controllers and filters for fuzzy systems and hybrid systems is the aim of this project. The project intends to analyze the influence of non-linearities, such as actuator saturation, on the dynamics of those systems, in addition to extend the developed methods to cope with the class of positive systems, important in the study of biological systems, for instance. Both continuous- and discrete-time systems are addressed, using the $\mathcal{H}_2$ and $\mathcal{H}_\infty$ norms as performance indices. Approaches based on homogeneous polynomial Lyapunov functions of arbitrary degree and convergent relaxations are employed, seeking, whenever possible, to formulate the addressed problems in terms of Linear Matrix Inequalities. The developed methods are evaluated by means of numerical simulations and the obtained results are compared with others available in the literature. (AU)