Studies On The Robust Control Of Uncertain Fractional Order Systems

The theory of fractional order calculus is the extension of the theory of integerorder calculus, the study of fractional calculus in mathematics has a history of morethan300years. It has been found that more accurate results can be obtained by apply-ing fractional calculus into system modelling in practical systems like new electricalelement, viscoelastic material, thermal difusion process, etc. Great attention has beenpaid into the fractional order control theory since fractional calculus was introduced tocontroltheoryat1990s. Andduetotheinevitableuncertaintyduringsystemmodelling,robust control is always an important research area in control theory.Robust control of fractional order system is a new research feld. This paper in-vestigates the robust stability condition of uncertain fractional order system and therobust stabilizability condition in the case of state feedback controller. For fractionalorder control system, polytopic uncertainty and norm-bounded uncertainty are consid-ered. Also, the robust control of singular fractional order system and incommensuratefractional order system is studied in this paper. The main contents of this paper are asfollows:1.Fractional calculus and existed researches in the feld of fractional order con-trol theory are briefy illustrated. Sufcient and necessary conditions for the stabilityof fractional order system with fractional order and are givenrespectively.2.Newsufcientconditionsfortherobuststabilityandrobuststabilizationofpoly-topic fractional order system are given to obtain less conservative results by means ofconstructing parameter dependent matrices.3.The robust control of uncertain fractional order system with-norm uncertainty and-norm uncertainty is studied. Problem of robust stabilizable bound for norm-bounded fractional order system by casting it into a generalized eigenvalue problem.4.Severalsufcientandnecessaryconditionsfortheadmissibilityofsingularfrac-tional order system are presented, and the robust admissibility of uncertain singularfractional order system is studied correspondingly.5.Therobuststabilityand stabilizationof intervaluncertainincommensuratefrac-tional order system are considered using new sufcient conditions for the stability ofincommensurate fractional order system given in this paper.