H_? Control Synthesis For Fractional System Over Finite Frequency Domain

Recently, due to the modern control system is getting larger and larger, and the frequency range of the system more accurate, the reduction theory over finite frequency domain is always a burgeoning area and have attracted many attentions. At present, great developments and wide applications have been made in positive systems. However, reduction theories over finite frequency domain on fractional-order systems are poor. So. this thesis mainly focuses on the H? model reduction and static output feedback control problem for fractional-order systems over finite frequency domain. The contributions and achievements are detailed below.1. The problem of model reduction over finite frequency domain for the fractional-order system is investigated. Firstly, by using matrix operation, the error system will be deformed, and the model reduction matrices will be-decoupled with the system matrices. Secondly, by virtue of the generalized K Lemma of fractional-order system, the bounded real Lemma of the error system over finite frequency domain is presented in terms of linear matrix inequalities, then the necessary and sufficiency conditions are given to ensure the existence of the desired H^ model reduction axt low. middle and high frequencies of fractional-order system. Then, by using matrix congruence transformation, the designed method of the desired H? model reduction will be given. Moreover, an iterative convex optimization algorithm is developed to solve the conditions. Finally, the numerical example shows the effectiveness of the proposed methods.2. The problem of designing the static output feedback controller over finite frequency domain for the fractional-order system is investigated. Firstly, based on the generalized KYP Lemma of fractional-order system, the bounded real Lemma of close-loop system over finite frequency domain is presented in terms of linear matrix inequalities, then the necessary and sufficiency conditions are given to ensure the existence of the desired H? static output feedback controller at low. middle and high frequencies of fractional-order system. By using the matrix congruence transformation, the designed method of the desired Hx static output feedback con-troller will be given. And two iterative linear matrix algorithms are developed to solve this problem. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.