Probabilistic robust stabilization of fractional order systems with interval uncertainty

Baris Baykant Alagoz; Celaleddin Yeroglu; Bilal Senol; Abdullah Ates

doi:10.1016/j.isatra.2015.01.003

Probabilistic robust stabilization of fractional order systems with interval uncertainty

ISA Trans. 2015 Jul:57:101-10. doi: 10.1016/j.isatra.2015.01.003. Epub 2015 Feb 7.

Authors

Baris Baykant Alagoz¹, Celaleddin Yeroglu², Bilal Senol², Abdullah Ates²

Affiliations

¹ Department of Electrical and Electronics Engineering, Inonu University, Turkey. Electronic address: baykant.alagoz@inonu.edu.tr.
² Department of Computer Engineering, Inonu University, Turkey.

PMID: 25666102
DOI: 10.1016/j.isatra.2015.01.003

Abstract

This study investigates effects of fractional order perturbation on the robust stability of linear time invariant systems with interval uncertainty. For this propose, a probabilistic stability analysis method based on characteristic root region accommodation in the first Riemann sheet is developed for interval systems. Stability probability distribution is calculated with respect to value of fractional order. Thus, we can figure out the fractional order interval, which makes the system robust stable. Moreover, the dependence of robust stability on the fractional order perturbation is analyzed by calculating the order sensitivity of characteristic polynomials. This probabilistic approach is also used to develop a robust stabilization algorithm based on parametric perturbation strategy. We present numerical examples demonstrating utilization of stability probability distribution in robust stabilization problems of interval uncertain systems.

Keywords: Fractional order sensitivity; Fractional order system; Robust stability analysis; System stabilization.