Robustness analysis of linear periodic time-varying systems subject to structured uncertainty

• Published in: Systems & control letters Vol. 55; no. 9; pp. 719 - 725
• Main Authors: Kim, Jongrae, Bates, Declan G., Postlethwaite, Ian
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2006; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Floquet theory; Lifting; Linear periodic time varying system; Robustness analysis; Floquet theory; Robustness analysis; Lifting; Linear periodic time varying system; Linear form; Worst case method; Linear fractional transformation; Linear time; Floquet method; Structured singular value; Time varying system; Linear time invariant system; Uncertain system; Robustness; Periodic system
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2006.02.005

In this paper, we show how Floquet theory may be combined with a technique known as Lifting to cast a linear periodically time-varying system subject to structured linear time invariant uncertainty in the form of a linear fractional transformation. The stability and performance robustness of the resulting system may then be analysed using standard μ -analysis methods. A significant advantage of the proposed approach is that it allows the computation of a worst-case destabilising uncertainty combination which may be used to estimate the conservatism of the computed robustness margin. An example is given to illustrate the application of the proposed approach.