# Application of Circle Criterion for Stability Analysis of Nonlinear Fractional Order System

Marta Zagórowska* and Wojciech Mitkowski

The purpose of this work is to examine the possibilities of using circle criterion for stability analysis of nonlinear system of fractional order. Analytical and numerical approach is prepared for some Lure’s systems. First we consider a nonlinear system $D^\alpha x(t) = f(t,x(t))$. Then it is linearized and we apply the circle criterion to check the stability of the system.

Mathematics Subject Classification: 34D20

Keywords: fractional differential equations; stability; circle criterion; Lure's system

Minisymposion: Fractional Order Calculus: Applications in Modeling and Control