Robust Stability Of Linear Time-Invariant Interval Fractional-Order System

This paper provides new analytical robust stability checking methods offractional-order linear time invariant(FO-LTI) interval uncertainty systemand extendsthe result already stated to fractional order interval polynomial systems.The mainpurpose if checking robust stability by system matrix which is uncertain,including thefolling content:1. The first chapter introduces the source of the problem, the significance of thestability of fractiona-order linear time invariant interval systems, the existed work andthe concept of the robust stability for FO-LTI interval systems and the concept of theFO-LTI interval systems.2. Based on [YangQuan Chen,Hyo-Sung Ahn, I.Pdolubny,Robust stability check offractional-order linear time invariant systems with interval uncertainties,in:Proceedingsof the IEEE Conference on Mechatronids and Automation, Niagara Falls, Canada,July,2005,pp.210-215] where matrix perturbation theory was used.For the new robuststability checking,Lyapunov inequality is utilized for finding the maximum eigenvalueof a Hermitian mxtrix.Thtough numical examples,the usefulness and the effectivenessof the newly proposed method are verified.3. This chapter tersents a necessary and sufficient robust stability condition offractional-order interval linear time invariant systems.The state matrix is considered aparametric interval uncertain matrix and fractional commensurate order is consideredbelonging to12.Using existence condition of HermitianP P*for complexLyapunov inequality,we show that a fractional-order interval linear system is robust stable if andonly if there exist Hermitian matricesP P*such that complex Lypunov inequalities are satisfiedfor all vertex matrices,which is a set of selected matrices.Two numerical examples are presented toverify the validity of the proposed approach.4. The robust stability of fractional-order interval polynomial systems arediscussed in this chapter.The result of the third chapter is exiended to fractional-orderinterval polynomial systems.The polynomial cannot be directly transformed into thecommensurate form.By some transformation,the robust stability can be directly examined using the companion matrix.