The Problem Of Designing Of H_∞Controller For Fractional Order Singular Systems

Fractional order systems are repented by differential equations with non-integer order. It has been found that the behavior of many physical systems can be more properly described by fractional-order systems than integer-order models. Singular system is a kind of system which has more extensive form than a normal system. For singular system, the state space model is the combination of algebraic expression and differential expression, which describe the dynamic characteristics and the static relationship of the state variables. Now many scholars study the fractional order system, and there have been many results, but the study of fractional order singular system is still in the primary stage. In this paper, H∞control problems for fractional-order singular systems, interval and polytope uncertainty fractional-order singular systems are studied. The contents are as follows:1)H∞control problem for fractional-order singular systems is studied. First, the bounded real lemma of fractional-order singular systems is presented, and the lemma give a necessary and sufficient condition which ensure the stability of fractional order singular system and satisfy H∞norm condition, then H∞output feedback controller for fractional order singular systems is designed. Finally, an example is used to demonstrate the validity of the result.2)H∞control problem for interval fractional-order singular systems is studied. This part presents a necessary and sufficient condition which ensure the existence of H∞control problem for interval fractional-order singular systems and H∞static feedback controller parameters for interval fractional-order singular systems is designed. Finally, an example is used to demonstrate the validity of the result.3)H∞control problem for polytope uncertainty fractional-order singular systems is stud-ied. From the bounded real lemma of fractional-order singular systems, a sufficient condition which ensure the existence of H∞control problem for polytope uncertainty fractional-order sin- gular systems is gived and H∞static feedback controller parameters for polytope uncertainty fractional-order singular systems is designed.Finally, an example is used to demonstrate the validity of the result.