In this work, we present the design of an observer for Takagi-Sugeno fuzzy systems with unmeasurable premise variables. Moving away from Lipschitz-based and L2 attenuation-based methods — which fall short in eliminating the mismatching terms in the estimation error dynamics — we leverage the differential mean value theorem. This approach not only removes these terms but also streamlines the factorization of the estimation error dynamics, making it directly proportional to the estimation error. To ensure the asymptotic convergence of the estimation error, we apply the second Lyapunov theorem, which provides sufficient stability conditions described as linear matrix inequalities. A numerical example applied on Three-tank hydraulic system is presented to demonstrate the observer's effectiveness.
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Observer Design for Takagi-Sugeno Fuzzy Systems with Unmeasurable Premise Variables based on Differential Mean Value Theorem
Published:
15 November 2023
by MDPI
in 10th International Electronic Conference on Sensors and Applications
session Robotics, Sensors and Industry 4.0
Abstract:
Keywords: Takagi-Sugeno Systems; nonlinear systems; Fuzzy observer; Mean value theorem.
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