Finite frequency H∞ control design for nonlinear systems

The work deals finite frequency H∞ control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H∞ lower can be by our method obtained developed where further comparison.

INTRODUCTION Fuzzy models [1] it generated widespread interest from engineers, mainly for renowned T-S systems my actually approach great category for non linear models. Then, the T-S systems is its universal approximation of a smooth non linear function by a family of IF and THEN non linear rules that represent the output/ input relationships of the models [2]- [11].
The interest of the literature mentioned above the H ∞ control design in the FF range. whereas, in such cases, standard design methods of full frequency range can provide conservatism. Nevertheless, in an actual application, the design characteristics are generally given in selector Frequency domains (see, [12]- [21]).
In this work, we develop new our method concerning FF design of nonlinears continuous systems. Using theadequate conditions are developed, ensuring that the closed loop system is stable. Numerical examples are provides to prove the effectiveness of FF propose method. Notations :

PDC CONTROLLER SCHEME
The fuzzy control as follows: then, we have the closed loop model:ẋ with problem formulation Given: the state feedback in the form of (5) such that: with is given in Table 1.
and n r=1 n s=1 λ r λ s Ω rs < 0 with Π is given of Table 1.

CONCLUSION
We sent the FF state feedback design. To reduce the closed-loop system and establish less conservative results, we have considered two practical examples has been provides to show the feasibility of tuning FF H ∞ fuzzy control design method.