Design of unknown input observer for discrete-time Takagi Sugeno implicit systems with unmeasurable premise variables

Essabre, Mohamed
Hmaiddouch, Ilham
El Assoudi, Abdellatif
El Yaagoubi, El Hassane

Bulletin of Electrical Engineering and Informatics
Vol 12, No 1: February 2023

In this study, an unknown input observer (UIO) is developed in explicit form to estimate unmeasurable states and unknown inputs (UIs) for nonlinear implicit systems represented by the discrete-time Takagi-Sugeno implicit systems (DTSIS) in the case of unmeasurable premise variables. The method employed is based on singular value decomposition (SVD) and augmenting the state vector, which is formed partly by the system state and partly by the UIs. The convergence of the augmented state estimation error is provided by a Lyapunov function ending with solving the linear matrix inequalities (LMI). An application to a model of the rolling disc is considered to evaluate the effectiveness of the developed approach. It appears that estimated variables converge to the true variables quickly and accurately.