LMI-based robust control of fractional-order uncertain linear systems. (English) Zbl 1228.93087

Summary: We are concerned with the method of observer-based control and static output feedback control for fractional-order uncertain systems with the fractional commensurate order \(\alpha\)(\(0<\alpha <1)\) and \(\alpha\)(\(1\leq \alpha <2)\) via linear matrix inequality (LMI) approach, respectively. First, the sufficient conditions for robust asymptotical stability of the closed-loop control systems are presented. Next, by using matrix’s singular value decomposition (SVD) and LMI technics, the existence condition and method of designing a robust stabilizing controller for such fractional-order control systems are derived. Unlike previous methods, the results are obtained in terms of LMI, which can be easily obtained by Matlab’s LMI toolbox. Finally, two numerical examples demonstrate the validity of this approach.


93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
34A08 Fractional ordinary differential equations
93C42 Fuzzy control/observation systems


Matlab; LMI toolbox
Full Text: DOI


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