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A separation principle for Takagi-Sugeno control fuzzy systems

Hadj Taieb N., Hammami M. A., Delmotte F.

Archives of Control Sciences

2019

Vol. 29, No. 2

227--245

An important application of state estimation is feedback control: an estimate of the state (typically the mean estimate) is used as input to a state-feedback controller. This scheme is known as observer based control, and it is a common way of designing an output-feedback controller (i. e. a controller that does not have access to perfect state measurements). In this paper, under the fact that both the estimator dynamics and the state feedback dynamics are stable we propose a separation principle for Takagi-Sugeno fuzzy control systems with Lipschitz nonlinearities. The considered nonlinearities are Lipschitz or meets an integrability condition which have no influence on the LMI to prove the stability of the associated closed-loop system. Furthermore, we give an example to ullistrate the applicability of the main result.

LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms

Krokavec D., Filasová A.

Archives of Control Sciences

2014

Vol. 24, no. 1

39--52

The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.