Moze, Mathieu; Sabatier, Jocelyn; Oustaloup, Alain LMI characterization of fractional systems stability. (English) Zbl 1125.93051 Sabatier, J. (ed.) et al., Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Dordrecht: Springer (ISBN 978-1-4020-6041-0/hbk; 978-1-4020-6042-7/e-book). 419-434 (2007). Summary: The notions of linear matrix inequalities (LMI) and convexity are strongly related. However, with state-space representation of fractional systems, the stability domain for a fractional order \(\nu\), \(0<\nu< 1\), is not convex. The classical LMI stability conditions thus cannot be extended to fractional systems. In this paper, three LMI-based methods are used to characterize stability. The first uses the second Lyapunov method and provides a sufficient but nonnecessary condition. The second and new method provides a sufficient and necessary condition, and is based on a geometric analysis of the stability domain. The third method is more conventional but involves nonstrict LMI with a rank constraint.For the entire collection see [Zbl 1116.00014]. Cited in 22 Documents MSC: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93D99 Stability of control systems 26A33 Fractional derivatives and integrals 93B50 Synthesis problems Keywords:linear matrix inequalities; LMI stability conditions PDFBibTeX XMLCite \textit{M. Moze} et al., in: Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Dordrecht: Springer. 419--434 (2007; Zbl 1125.93051) Full Text: DOI