A STATE-SPACE APPROACH TO DYNAMIC STABILITY OF FRACTIONAL-ORDER SYSTEMS: THE EXTENDED ROUTH-HURWITZ THEOREM

This paper considers the case of Beck’s column, a linear elastic cantilever columnsubjected to a constant follower load at its free end. The column foundation is modeled as bed ofhereditary elements that react with a vertical force distributed along the beam axis. The reactingsupports are modeled with spring-pot element that is a two parameters mechanical elements(C; ) with an intermediate behavior between spring and dashpot. The constitutive equation ofthe spring-pot involves the so called fractional order derivatives and dynamic stability problemin presence of fractional-order operator must be faced for the Beck’s column. In this study ,the authors generalize Routh-Hurwitz theorem of stability on the fractional order differentialequation (FODE), system that governs the dynamic stability. Some numerical examples hasbeen reported in the paper for two-degree of freedom system.