An algebraic stability test for fractional order time delay systems

Abstract

In this study, an algebraic stability test procedure is presented for fractionalorder time delay systems. This method is based on the principle of eliminatingtime delay. The stability test of fractional order systems cannot be examineddirectly using classical methods such as Routh-Hurwitz, because such systemsdo not have analytical solutions. When a system contains the square roots ofs, it is seen that there is a double value function of s. In this study, a stabilitytest procedure is applied to systems including ps and/or different fractionaldegrees such as s where 0 < α < 1, and αǫR. For this purpose, the integerorder equivalents of fractional order terms are first used and then the stabilitytest is applied to the system by eliminating time delay. Thanks to the proposedmethod , it is not necessary to use approximations instead of time delay termsuch as Pad´e. Thus, the stability test procedure does not require the solutionof higher order equations.