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| Author(s): |
Eduardo Stockler Tognetti
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação |
| Defense date: | 2011-12-20 |
| Examining board members: |
Pedro Luis Dias Peres;
Marcelo Carvalho Minhoto Teixeira;
Vilma Alves de Oliveira;
Akebo Yamakami;
Fernando Antonio Campos Gomide
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| Advisor: | Ricardo Coração de Leão Fontoura de Oliveira; Pedro Luis Dias Peres |
| Abstract | |
This thesis proposes, as main contribution, new linear matrix inequalities conditions for stability analysis and control synthesis of continuous and discrete-time Takagi-Sugeno fuzzy systems. A state feedback control law is considered and, for continuous-time systems, static and dynamic output feedback controllers of arbitrary order are also determined. The H2 and H? guaranteed costs are adopted as performance criteria. The proposed Lyapunov functions, more general than the others in the literature, are constructed as fuzzy combinations of quadratic in the state functions that are homogeneous polynomials of arbitrary degree depending on the membership functions of the fuzzy systems. The membership functions are modeled in a space defined by the Cartesian product of simplexes in the same instant of time, in the continuous-time case, or in multiple instants of time, yielding finite memory controllers depending on the present and past parameters, in the discrete-time case. In the continuous-time synthesis conditions, the premise variables used in the control law can be defined by the designer, accordingly to real-time availability, as a selective feature of the controller. Two different situations are considered in terms of the rates of variation of the membership functions. A convex set models the space of the timederivatives of the membership functions if some upper bounds of the variation rates are known. For arbitrary rates, when the premise variables are the states of the system, a line-integral Lyapunov function is considered associated with a two steps procedure. At the first step, a state feedback is computed and used as an input for the second step, that provides, if possible, a state feedback controller that take into account more stringent performance specifications, or static or dynamic controllers, of full and reduced orders. Numerical examples illustrate the results, showing that the proposed approaches can be less conservative and more efficient when compared with other methods available in the literature (AU) | |
| FAPESP's process: | 10/18960-2 - LMI relaxations for Takagi-Sugeno fuzzy systems control design |
| Grantee: | Eduardo Stockler Tognetti |
| Support Opportunities: | Scholarships in Brazil - Doctorate |