Studies On The Robust H_? Control Of Uncertain Fractional Order Systems

Fractional order calculus is a natural generalization of the theory of integer order calculus,it computes fractional differential and fractional integral for functions.As fractional calculus is more accurate and more concise in describing some physical systems,fractional order control system is becoming one of the hot topics in the academic field.At the same time,in the pro-cess of mathematical modeling for a real physical system,a control system will inevitably be uncertain due to various reasons such as the limitation of measurement accuracy and the simpli-fication of complex conditions,therefore,the robust control analysis and synthesis of uncertain system has been a focus in the research of automatic control theory.In this paper,we study the robust H_?control for uncertain fractional order systems,the two most common types of uncertainty,namely,polytopic uncertainty and norm-bounded uncertainty,are considered,the problems discussed include the robust H_?control for uncertain systems,the H_?model reduc-tion for uncertain systems,the robust H_?filtering for uncertain systems,and the robust H_?decentralized control for interconnected systems.Specific contents are as follows:1.Several common definitions of fractional calculus and the research status of fractional order control system are introduced,some typical uncertain expression forms of uncertain con-trol system are listed,what's more,the necessary knowledge to discuss the robust H_?control of uncertain fractional order systems is introduced.2.The robust H_?control for fractional order systems with polytopic uncertainty is studied.The method of dealing with uncertainty in the integer order system is used,based on the H_?bounded real lemma for commensurate fractional order control system,two H_?performance criteria for fractional order systems with polytopic uncertainty are proposed,and two robust H_?state feedback control laws for fractional order systems with polytopic uncertainty are obtained.3.The H_?model reduction for fractional order systems with polytopic uncertainty is dis-cussed.According to the H_?bounded real lemma of commensurate fractional order control systems,the problem of the H_?model reduction for fractional order systems with polytopic uncertainty is transformed into the problem of solving a set of LMI conditions.A lower or-der stable fractional order system model for approximating the higher order uncertain fractional order system is given,which confirms that the augmented system satisfies a prescribed H_?performance requirements.4.The robust H_?filtering for fractional order systems with polytopic uncertainty is pre-sented.From the definition of H_?norm of the system transfer function,a new expression of the H_?bounded real lemma for commensurate fractional order control systems is given,with the advantages of this expression,a full order filter construction method for fractional order sys-tems with polytopic uncertainty is given,and it is transformed into the feasible solution solving process of linear matrix inequalities.5.The Robust H_?decentralized control for fractional order interconnected systems with norm-bounded uncertainty is studied.With the definition of positive definite matrix and neg-ative definite matrix,on the basis of the H_?bounded real lemma of commensurate fractional order control systems,the H_?performance criterion for fractional order interconnected systems with norm-bounded uncertainty is proposed,and then the robust H_?decentralized state feed-back control law for fractional order interconnected systems with norm-bounded uncertainty is obtained.