Stability Criteria for the Control of Multi-Fractional-Order Systems with Multiple State Delays

This paper aims to investigate a multiple fractional derivative order system control with multiple delays. The generalized Lyapunov function and YkP lemma are used to obtain algebraic and frequency criteria for asymptotic stability for these systems. Linear fractional systems and linear systems with nonlinear components are analyzed. Frequency criteria are represented graphically by polar plots. In contrast to classical Popov-type polar plots, where the critical point is determined by the system’s nonlinearity, in fractional-order systems, the critical point of the polar plots is determined by the fractional order. Numerical applications highlight the investigation techniques and the particularities of the presented criteria.