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An observer design for Takagi-Sugeno fuzzy bilinear control systems

Delmotte François, Hadj Taieb Nizar, Hammami Mohamed Ali, Meghnafi Houria

Archives of Control Sciences

2023

Vol. 33, No. 3

631--649

In this paper, the observer design problem for a T-S fuzzy bilinear control system is investigated. First, an observer of Kalman type is designed to estimate the system states for the linear case. Then, some new sufficient conditions are derived to show the exponential convergence of the solutions of the error equation for fuzzy bilinear systems. Furthermore, we consider some uncertainties of the system that are bounded and satisfy a certain condition where an observer is designed. Moreover, an application to Van de Vusse system is given.

Stability analysis and design of state estimated controller for delay fuzzy systems with parameter

Hadj Taieb Nizar, Hammami Mohamed Ali, Delmotte François

Archives of Control Sciences

2022

Vol. 32, No. 4

709--731

This paper deals with the problem of stabilization by an estimated state feedback for a family of nonlinear time-delay Takagi-Sugeno fuzzy parameterized systems. The delay is supposed to be constant where the parameter-dependent controls laws are used to compensate the nonlinearities which are formulated in terms of linear matrix inequalities (LMIs). Based on the Lyapunov-Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. The controller and observer gains are able to be separately designed even in the presence of modeling uncertainty and state delay. Finally, a numerical example is given to show the applicability of the main result.