Reducing conservatism in robust stability analysis of fractional-order-polytopic systems.

This paper studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore system's robust stability through investigating the robust stability of these LOPCPs based on the exposed edges idea. For the sake of feasibility comparison, extensive examples are elaborated that reveal the superiority of the proposed algorithm. • The stability of fractional-order systems with polytopic uncertainty is assessed. • The design space is divided to simplexes and the proposed algorithm searches them. • The direct searching method checks the robust stability of each simplex. • In each simplex, a local over-parameterized characteristic polynomial is generated. • The robust stability (RS) of local simplexes guarantees the RS of the main system. [ABSTRACT FROM AUTHOR]