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

Yosr Garbouj (1) , Thach Ngoc Dinh (2) , Talel Zouari (3) , Moufida Ksouri (1) , Tarek Raïssi (2)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis
2 CEDRIC - LAETITIA - CEDRIC. Traitement du signal et architectures électroniques
3 ESPRIT - Ecole Supérieure Privée d'Ingénierie et de Technologies

This 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.

Keywords: Nonlinear switched system; Takagi-Sugeno models; unmeasurable premise variables; stability; robustness; interval observer design

Domains: Automatic

Yosr Garbouj, Thach Ngoc Dinh, Talel Zouari, Moufida Ksouri, Tarek Raïssi. Interval estimation of switched Takagi-Sugeno systems with unmeasurable premise variables. 5th IFAC Conference on Intelligent Control and Automation Sciences, IFAC, Aug 2019, Belfast, United Kingdom. pp.73-78, ⟨10.1016/j.ifacol.2019.09.120⟩. ⟨hal-02434057⟩