Robust stability testing function for a complex interval family of fractional-order polynomials

Abstract

The robust stability of a family of interval fractional-order systems with complex coefficients is investigated in this study. The concept of “a family of interval fractional-order systems with complex coefficients” means that the characteristic function of a control system can be of both commensurate and non-commensurate orders, the coefficients of the characteristic function can be uncertain parameters, and may be complex numbers. At first, a simple graphical procedure is presented for robust stability analysis. The “robust stability testing function” is then extended to look at the robust conditions. To the best of the authors’ knowledge, no auxiliary function for analyzing the robust stability of the systems under investigation has been introduced until now. Moreover, lower and upper frequency bounds are provided which are useful to improve the computational efficiency of testing the robust stability conditions. Eventually, to verify the results, analytical examples and numerical simulations are provided.