A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems

• Published in: Automatica (Oxford) Vol. 41; no. 11; pp. 1933 - 1941
• Main Authors: Ebihara, Yoshio, Hagiwara, Tomomichi
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.11.2005; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Dilated linear matrix inequalities; Exact sciences and technology; Real parametric uncertainty; Robust performance analysis; Robust performance analysis; Dilated linear matrix inequalities; Real parametric uncertainty; Robust control; Uncertainty; Linear time invariant system; Uncertain system; Linear matrix inequality; Parameter; Performance analysis
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2005.05.023

This paper studies robust performance analysis problems of linear time-invariant systems affected by real parametric uncertainties. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is know that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated LMI conditions even in the case of rational parameter dependence. In particular, it turns out that the proposed dilated LMIs enable us to assess the robust performance via multiaffine parameter-dependent Lyapunov variables so that less conservative analysis results can be achieved. Connections among the proposed conditions and existing results are also discussed concretely. Several existing results can be viewed as particular cases of the proposed conditions.