Noncommensurate Constant Orders as Special Cases of DOLTIS

Abstract

Stability is a minimum requirement for control systems, certainly including fractional-order systems. The stability results on fractional-order linear time-invariant (FO-LTI) systems with commensurate orders were presented for the first time, it permits to check the asymptotically stability through the location of the system matrix eigenvalues of the pseudo state space representation of fractional-order system in the Complex plane. Henceforth, there were some systematic results on the robust stability of interval uncertain FO-LTI systems. The BIBO-stability of fractional-order delay systems of retarded and neutral types was studied and sufficient conditions were presented for retarded type, and only sufficient conditions were provided for neutral type. Sufficient conditions of stability were provided for an important special case fractional-order delay system of neutral type. However, such theorems don’t permit to conclude the system stability without computing the system’s poles, which constitutes tedious work, so based on Cauchy’s integral theorem and by solving an initial-value problem, an effective numerical algorithm for testing the BIBO stability of fractional delay systems was presented.