Probabilistic robust stabilization of fractional order systems with interval uncertainty. (July 2015)

• Record Type: Journal Article
• Authors: Alagoz, Baris Baykant; Yeroglu, Celaleddin; Senol, Bilal; Ates, Abdullah
• Is Part Of: ISA transactions. Volume 57(2015:Jul.)
• Page Start: 101
• Page End: 110
• Publication Date: 2015-07
• Subjects: Fractional order system -- Robust stability analysis -- System stabilization -- Fractional order sensitivity; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2015.01.003
• Languages: English
• ISSNs: 0019-0578

Abstract

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. Highlights: This study presents a probabilistic method for robust stability analysis. Stability probability is analyzed for fractional order interval systems. Robust stability ranges are determined by probabilistic analyses. These analyses are used to parametric robust stabilization. Simulation examples illustrate robust stable fractional order system design.