Robust stabilization and observation of positive Takagi-Sugeno systems

Esta tesis propone metodologías para diseñar controladores robustos y observadores para los sistemas positivos descritos por modelos de Takagi-Sugeno (TS), lineal, inciertos, y tal vez con retraso. Las condiciones de síntesis se expresan como LMIs (desigualdades matriciales lineales). En la primera parte, se establecen las condiciones para garantizar la estabilización asintótica y la α-estabilización de los sistemas T-S lineales positivas y, tal vez afectados por incertidumbres de intervalo, usando controladores de retroalimentación de estado descompuestos. En la segunda parte, se dan las condiciones necesarias y suficientes para la estabilización de los sistemas de T-S positivos con retraso, en dos casos: cuando las variables de premisa del sistema son medibles o no. Además, el problema de diseño de control basado en observador es considerado, por las leyes de retroalimentación del estado que se pueden elegir con o sin memoria. Para mostrar la eficacia de los métodos propuestos, se proporcionan ejemplos numéricos y prácticos, dando resultados satisfactorios.Departamento de Ingeniería de Sistemas y Proceso

Observer design for Takagi-Sugeno Lipschitz systems affected by disturbances using quadratic boundedness

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this paper, a proportional observer design using quadratic boundedness is proposed in order to estimate the state of a system described by a Takagi-Sugeno model with a Lipschitz nonlinearity term, and affected by unknown disturbances. The conditions for ensuring that the error between the real and the estimated state converge within an ellipsoidal region about zero, are provided in the form of a linear matrix inequality (LMI) formulation. Then, the simulation results of this approach applied to a four-wheeled omni-directional mobile robot will be shown.Peer ReviewedPostprint (author's final draft

Takagi-Sugeno fuzzy observer for a switching bioprocess : sector nonlinearity approach

Mexican Consejo Nacional de Ciencia y Tecnología (CONACyT)

Interval estimation of switched Takagi-Sugeno systems with unmeasurable premise variables

International audienceThis paper deals with interval observers design for nonlinear switched systems. The nonlinear modes are represented by the Takagi-Sugeno (T-S) fuzzy models with premise variables depending on unmeasurable terms, e.g. the state vector. This T-S structure can be used to represent exactly a nonlinear switched system in a compact set of the state space. The introduced method in this paper allows to compute the lower and upper bounds of the system state under the assumption that the disturbances as well as the measurement noises are unknown but bounded. First, the stability conditions of the proposed T-S interval observers are developed via Linear Matrix Inequality (LMI) formulations to ensure the convergence of the nonnegative observation error dynamics. Then, changes of coordinates are employed to relax the restrictive requirement of nonnegativity constraints. Theoretical results are applied to a numerical example to illustrate the effectiveness of the proposed method