In the present paper stabilization of a class of fractional-order unstable delay systems by fractional-order controllers is investigated. To derive the sufficient conditions for stability, an analysis based on the Nyquist stability criterion has been adopted. The analysis is carried out with fractional-order [proportional–integral] and [proportional–derivative] controllers to obtain the upper bound for the time delay. Furthermore, the paper proposes the conditions on the parameters of the controllers which must be fulfilled in order to have a stabilized process. Two illustrated examples using fractional-order controllers are presented for demonstrating the proposed approach.

The stabilization of all-pole unstable systems with time delay by fractional-order controllers is investigated in this paper. Sufficient conditions for stabilizability by fractional-order [PD]/[PI] controllers are determined. To derive the conditions for stability, an analysis based on Nyquist stability criterion is adopted and the upper bound for the time delay is determined. Furthermore, this paper provides the stabilizing range of the controller parameters. Theoretical proofs in company with illustrative examples are also provided.

No abstract

This paper deals with the stability problem in LTI fractional order systems having fractional orders between 1 and 1.5. Some sufficient algebraic conditions to guarantee the BIBO stability in such systems are obtained. The obtained conditions directly depend on the coefficients of the system equations, and consequently using them is easier than the use of conditions constructed based on solving the characteristic equation of the system. Some illustrations are presented to show the applicability of the obtained conditions. For example, it is shown that these conditions may be useful in stabilization of unstable fractional order systems or in taming fractional order chaotic systems.

No abstract