Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems

Bulletin of the Polish Academy of Sciences. Technical Sciences

M. Bus?owiczCorresponding authorFaculty of Electrical Engineering, Bia?ystok University of Technology, 45D Wiejska St., 15-351 Bia?ystok, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹  A. RuszewskiFaculty of Electrical Engineering, Bia?ystok University of Technology, 45D Wiejska St., 15-351 Bia?ystok, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] Faculty of Electrical Engineering, Bia?ystok University of Technology, 45D Wiejska St., 15-351 Bia?ystok, Poland

关键词: Keywords : linear system;    discrete-time;    fractional;    practical stability;    asymptotic stability;   

DOI  :  10.2478/bpasts-2013-0084

学科分类：工程和技术（综合）

来源: Polska Akademia Nauk * Centrum Upowszechniania Nauki / Polish Academy of Sciences, Center for the Advancement of Science

【 摘 要 】

In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.

【 授权许可】

Unknown