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

Abstract

This paper considers the case of Beck’s column, a linear elastic cantilever column subjected to a constant follower load at its free end. The column foundation is modeled as bed of hereditary elements that react with a vertical force distributed along the beam axis. The reacting supports 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 of the spring-pot involves the so called fractional order derivatives and dynamic stability problem in 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 differential equation (FODE), system that governs the dynamic stability. Some numerical examples has been reported in the paper for two-degree of freedom system.