Novel robust stability conditions of fractional-order systems with structured uncertain parameters based on parameter-dependent functions: the 0<α<1 case

ABSTRACT

In this paper, the robust stability of fractional-order systems with fractional order $0<\alpha <1$ and structured uncertain parameters is considered. Firstly, novel robust stability conditions of the above systems are presented based on the parameter-dependent polynomial functions. Secondly, the existence of the parameter-dependent polynomial functions is transformed into linear matrix inequalities via the generalized Kalman-Yakubovič-Popov lemma. In addition, the above methods can also be applied to solve the robust stability of fractional-order systems with structured uncertainties or polytopic uncertainties. Finally, numerical examples are presented to show the proposed methods are less conservative than the existing methods.

KEYWORDS:

• Fractional-order system
• structured uncertain parameter
• robust stability
• linear matrix inequality

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is partially supported by the National Natural Science Foundation of China under Grants 62073217, 61374030 and 61533012.