Robust stability of fractional order system with polynomial uncertainties based on sum-of-squares approach

This paper concentrates on the study of robust stability of fractional order system with polynomial uncertainties. Polynomial uncertainties means that the coefficients of the fractional system are polynomial functions of the parameters, and the uncertain parameters vary in semialgebraic set. The roots of the fractional order characteristic function are assigned in the shifted half plane. Therefore, the fractional system can maintain certain robustness and time domain performance. In order to check the robust stability of fractional order polynomial system, alternative methods are presented by using Sum of Squares (SOS) programs. Since SOS programs can be all written as Linear Matrix Inequalities (LMI) feasibility tests, our proposed method embraces the advantages of LMI techniques. Numerical examples are presented to illustrate the proposed results. (c) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.