Global Stability of Nonlinear Feedback Systems with Fractional Positive Linear Parts

The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k₁e ≤ f(e) ≤ k₂e for some positive k₁ and k₂. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k₁, −1/k₂).