Exact Stability Test and Stabilization for Fractional Systems J. Y. Kaminski ∗ , R. Shorten † , and E. Zeheb ‡ Abstract In this paper we point out a connection between regular chains and the stability of fractional order systems. This observation leads to an elementary test for the stability of commensurate fractional systems. Keywords: Fractional order systems; Stability; Regular chains algorithms 1 Introduction We consider a fractional order system of the following from: d α X dt α = AX + BU Y = CX + DU (1) and transfer matrix H (s)= Y (s)U (s) -1 = C  s α I − A  -1 B + D, (2) * Department of Applied Mathematics, Faculty of Sciences, Holon Institute of Technology, Holon, Israel † Optimization, Control and Decision Science, IBM Research. Robert Shorten was supported in part by Science Foundation Ireland grant 11/PI/1177. ‡ Faculty of Sciences, Holon Institute of Technology,Holon, Israel and Department of Electrical Engineer- ing, Technion-Israel Institute of Technology,Haifa,Israel 1