Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability

Bulletin of the Polish Academy of Sciences. Technical Sciences

K.J. LatawiecCorresponding authorInstitute of Control and Computer Engineering, Opole University of Technology, 31 Sosnkowskiego St., 45-272 Opole, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹  R. Stanis?awskiInstitute of Control and Computer Engineering, Opole University of Technology, 31 Sosnkowskiego St., 45-272 Opole, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] Institute of Control and Computer Engineering, Opole University of Technology, 31 Sosnkowskiego St., 45-272 Opole, Poland

关键词: Keywords : Grünwald-Letnikov fractional difference;    discrete-time fractional-order systems;    stability conditions;    Cauchy’s argument principle;   

DOI  :  10.2478/bpasts-2013-0034

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 】

This paper presents a series of new results on the asymptotic stability of discrete-time fractional difference (FD) state space systems and their finite-memory approximations called finite FD (FFD) and normalized FFD (NFFD) systems. In Part I, new, general, necessary and sufficient stability conditions are introduced in a unified form for FD/FFD/NFFD-based systems. In Part II, an original, simple, analytical stability criterion is offered for FD-based systems, and the result is used to develop simple, efficient, numerical procedures for testing the asymptotic stability for FFD-based and, in particular, NFFD-based systems. Consequently, the so-called f-poles and f-zeros are introduced for FD-based system and their closed-loop stability implications are discussed

【 授权许可】

Unknown