Robust H_∞ Controller design based on Generalized Dynamic Observer for Uncertain Singular system with Disturbance

This paper presents a robust ∞_H controller design, based on a generalized dynamic observer for uncertain singular systems in the presence of disturbance. The controller guarantees that the closed loop system be admissible. The main advantage of this method is that the uncertainty can be found in the system, the input and the output matrices. Also the generalized dynamic observer is used to estimate the states of system. This type of observer increases the steady state accuracy because of the integral term, and because of the dynamic term, it has a higher estimation speed than proportional-integral observers. First, the necessary conditions for existence a generalized dynamic robust observer are presented and some coefficients matrices of the observer are computed so that the estimation error asymptotically converges to zero. Then, the robust ∞_H controller is designed using state feedback in order to guarantee that the closed loop system is admissible. The existence conditions of the observer and the controller are given simultaneously using suitable Lyapunov function. Moreover, existing inequalities are transformed into linear matrix inequalities (LMI) using a set of algebraic relations, and by solving these LMIs, the coefficients of the observer and the controller are obtained. Finally, by presenting an algorithm, the computational method will be expressed in a systematic way, and a numerical example demonstrates the efficacy of the proposed method.