2019 # Robust stabilizability of fractional order proportional integral controllers for fractional order plants with uncertain parameters: A new value set based approach

**Abstract:** In this paper, a new value set based approach is presented to study the robust stability of a fractional order plant with parametric uncertainty of the interval type by using a fractional order proportional integral controller. The concept of interval uncertainty means that the parameters of the system transfer functions are uncertain parameters that each adopts a value in a real interval. Based on the zero exclusion principle, it is necessary to check whether the value set of the characteristic polynomial for…

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“…Remark 3: Consider the interval uncertainties for only the coefficients of the fractional order quasi-polynomial (1) such as the fractional order polynomial (4) studied in Gao (2015) and Ghorbani and Tavakoli-Kakhki (2019). Theorem 1 confirms that (4) is robust stable, which is the same as the obtained result in Gao (2015) and Ghorbani and Tavakoli-Kakhki (2019).…”

confidence: 72%

“…Remark 3: Consider the interval uncertainties for only the coefficients of the fractional order quasi-polynomial (1) such as the fractional order polynomial (4) studied in Gao (2015) and Ghorbani and Tavakoli-Kakhki (2019). Theorem 1 confirms that (4) is robust stable, which is the same as the obtained result in Gao (2015) and Ghorbani and Tavakoli-Kakhki (2019).…”

confidence: 72%

“…Generally, this method imposes a computational burden and is difficult to be used. Also, consider Example 1 in Gao (2015) and Ghorbani and Tavakoli-Kakhki (2019), which is…”

confidence: 99%