Title of article :
An algebraic stability test for fractional order time delay systems
Author/Authors :
Mine ̈Ozyetkin, Munevver Department of Electrical and Electronics Engineering - Aydın Adnan Menderes University, Turkey , Baleanu, Dumitru Department of Mathematics - Faculty of Art and Sciences - Cankaya University, Turkey
Abstract :
In this study, an algebraic stability test procedure is presented for fractional order time delay systems. This method is based on the principle of eliminating time delay. The stability test of fractional order systems cannot be examined directly using classical methods such as Routh-Hurwitz, because such systems do not have analytical solutions. When a system contains the square roots of s, it is seen that there is a double value function of s. In this study, a stability test procedure is applied to systems including sqrt(s) and/or different fractional degrees such as s^alpha where 0 < ? < 1, and ? include in R. For this purpose, the integer order equivalents of fractional order terms are first used and then the stability test is applied to the system by eliminating time delay. Thanks to the proposed method, it is not necessary to use approximations instead of time delay term such as Pade. Thus, the stability test procedure does not require the solution of higher order equations.
Keywords :
Fractional order systems , pproximation , Time delay , Stability
Journal title :
International Journal of Optimization and Control: Theories and Applications