# Takagi-Sugeno Fuzzy Representation to Modelling and State Estimation

Abstract : This chapter shows the interest of Takagi-Sugeno (T-S) fuzzy model approach to apprehend nonlinear behaviors of physical systems and its application for observers design. From mathematical nonlinear model or experimental data, a T-S representation can be obtained using different techniques. This approach is largely exploited in many fields such as control, diagnosis and fault-tolerant control. Then the design of a robust T-S observer is addressed. The chapter considers a robust observer with respect to the uncertainties as well as unknown inputs. The synthesis of sufficient design conditions are performed using Lyapunov functions and set of linear matrix inequalities ($\mathcal{LMI}$). Two case studies are given. An example, dealing with a turbojet plane, shows how to obtain T-S representation using optimization algorithms. The validity of the proposed observer design is based on automatic steering of vehicles.
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Submitted on : Monday, November 29, 2021 - 3:29:11 PM
Last modification on : Tuesday, November 30, 2021 - 3:45:49 AM

### Identifiers

• HAL Id : hal-03455217, version 1

### Citation

Mohammed Chadli, Thierry-Marie Guerra, Ivan Zelinka. Takagi-Sugeno Fuzzy Representation to Modelling and State Estimation. Ivan Zelinka; Václav Snášel; Ajith Abraham. Handbook of Optimization : From Classical to Modern Approach, Springer, pp. 451-479, 2013, 978-3-642-30503-0. ⟨hal-03455217⟩

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