On τ ‐decomposition frequency‐sweeping strategy to rational‐order fractional systems with commensurate delays

Abstract

This study presents an effective analysis procedure to give the bounded input bounded output stability intervals of time delay for a class of commensurate delayed fractional-order systems with rational order. First, it is proposed that the analysis on multi-valued characteristic function of delayed fractional-order systems can be conducted equivalent on the consideration of the principal branch. The statement makes the generalisation of the τ -decomposition method in integer order case possible. With the convenience in studying delayed systems, the frequency-sweeping method is applied logically, and the PIRs and the cross-direction around them can be determined through the frequency-sweeping curves simultaneously. Moreover, the verification of the neutral stability condition of fractional-order delayed systems is considered in a systematic manner. At last, some examples show that the proposed strategy is practically useful in the analysis and design of feedback control for both integer and fractional-order systems with time delays.

Stability of neutral type fractional delay systems and its relation with stability of time‐delay and discrete systems

“…A necessary and sufficient condition has been proposed for BIBO‐stability of some large classes of the neutral type in [10]. Recently, the generalisation of the τ ‐decomposition method has been developed to analyse the BIBO stability of a large class of time‐delayed FOSs [11]. However, it is assumed that the system only have simple poles on the imaginary axis [11, Assumption 2].…”

“…Recently, the generalisation of the τ ‐decomposition method has been developed to analyse the BIBO stability of a large class of time‐delayed FOSs [11]. However, it is assumed that the system only have simple poles on the imaginary axis [11, Assumption 2].…”