| This thesis deals with the design of a fuzzy observer and a fuzzy controller for uncertain nonlinear systems.Using matched condition,the nonlinear system is represented through a set assumptions of matrix inequalities.By constructing a class of Lyapunov candidate and the matrix inequalities,the proposed controllers are designed to guarantee the stability of the whole closed-loop systems.New Ricatti equations are presented with the corresponding solv-ability conditions.The proposed approach is also in favor of applying separation principle to separately design the fuzzy observer and the fuzzy controller.Lastly,numerical simulations on an inverted pendulum on a cart are done showing the effectiveness of the approach.To evaluate the performance of the proposed controller,the controller is compared with the existing controller[1],designed using Linear matrix inequality(LMI)approach.The performance is analyzed in terms of the time response of the system when the proposed fuzzy observer and fuzzy controller is used to balance an inverted pendulum on a cart in comparison to the existing one[1].The proposed controller provides a better performance in respect to all the system time response parameters(Rise time,Settling time,Peak,Peak time,Overshoot,Undershoot).Next,the research is also concerned with the design of observer-based output feedback con-troller for T-S fuzzy systems with time-delay under imperfect premise matching.The pro-posed fuzzy controller and fuzzy observer do not need to share the same premise mem-bership functions and number of rules with T-S fuzzy systems,which makes the controller and observer design more flexible.Using a recently developed integral inequality,a delay-dependent method for the controller and observer design is provided.With the help of some advanced matrix inequalities,the proposed conditions are presented in the form of linear matrix inequalities(LMIs).Simulation example is done to show the effectiveness of the pro-posed controller. |
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