Contributions to analysis and control of takagi-sugeno systems via piecewise, parameter-dependent, and integral lyapunov functions
- GONZÁLEZ GERMÁN, IVÁN TEMOATZIN
- Antonio Sala Director/a
- Miguel Ángel Bernal Reza Director/a
Universidad de defensa: Universitat Politècnica de València
Fecha de defensa: 26 de marzo de 2018
- Fernando Tadeo Presidente
- J. V. Salcedo Secretario/a
- Kevin Guelton Vocal
Tipo: Tesis
Resumen
This thesis considers a Lyapunov-based approach for analysis and control of nonlinear systems whose dynamical equations are rewritten as a Takagi-Sugeno model or a convex polynomial one. These structures allow solving control problems via convex optimisation techniques, more specifically linear matrix inequalities and sum-of-squares, which are efficient tools from the computational point of view. After providing a basic overview of the state of the art in the field of Takagi-Sugeno models, this thesis address issues on piecewise, parameter-dependent and line-integral Lyapunov functions, with the following contributions: An improved algorithm to estimate the domain of attraction of nonlinear systems for continuous-time systems. The results are based on piecewise Lyapunov functions, linear matrix inequalities, and geometrical argumentations; level-set approaches in prior literature are significantly improved. A generalised parameter-dependent Lyapunov function for synthesis of controllers for Takagi-Sugeno systems. The approach proposed a multi-index control law that feeds back the time derivative of the membership function of the Takagi-Sugeno model to cancel out the terms that cause a priori locality in the Lyapunov analysis. A new integral Lyapunov function for stability analysis of nonlinear systems. These results generalise those based on line-integral Lyapunov functions to the polynomial framework; it turns out path-independency requirements can be overridden by an adequate definition of a Lyapunov function with integral terms.