We have discussed several topic, s on robust control in this paper. In the first part of the paper (chapter 2), the relations between weighting functions and closed loop system, controller has been investigated for mixed sensitivity problem. We find and prove that some zeros and/or polos of weighting functions will enter the sot of zeros and/or poles of closed loop system or controller under some conditons. This relation should be considered to choose weighting functions for a more successful robust control system design. In the second part of the paper (chapter 3), we discuss how to design H∞ controller based on chain scattering description of transfer function and (J,J') loseless factorizafion. Our main purpose is to overcome the difficulties of classical DGKF method. We investigate the computational problems, Q- parameter utilization problem, stable controller design problem and reduced order controller design problem. First, necessary and sofficient conditions of solvability are obtained for a matrix equation :XTJp,q X=S and a simple numerical algorithm is proposed. It is necessary to solve it to compute (J,J') loseless factorization in state space. The relation between the existence of Dπ and the assumption A2 in DGKF method is also discussed. Then we give a numerical algorithm to compute (J,J') loseless factorization in RL∞. Next state space parameterization of controller is obtained and we outline procedures to compute H∞ controller based on chain scattering description of transfer function and (J,J') loseless factorization. The state space paramoterization of controller is not only suitable to be used in computation of H∞ controller, but also suitable to be used in Q parameter utilization problem since it clearly reveals the relation between controller and Q(s). First we discuss the rehtion between the order of controller and Q(s). We find if deg(Q(s)=0, the order of controller will not increase when we introduce a nonzero Q parameter; if deg(Q(s)) > 0, the order of controller generally will increase. Then we discuss how to get stable controller, whose order does not increase at the same time, by constant matrix parameter Dq. Reduced order controller design is considered as an important problem in H∞ controll. In this paper we propose a method to get reduced order controller by parameter Q(s). The main idea is to cancell poles and zeros controller K(s) by Q(s). The key step is to find the cotmnon zeros of denominator and numerator of K(s). We find all possible common zeros tot SISO system and propose an algorithm to get Q(s). For MIMO system we give partial possible common zeros and also give an algorithm to compute Q(s). If one can get a Q(s) by our method, a n-th order controller will reduce at least to a (n-t)-th controller. Finally we have implemenated our algorithms in Matlab environment. Design examples of stable controller and reduced order c
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