Global Stability of Nonlinear Feedback Systems with Fractional Positive Linear Parts

Abstract

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).

Keywords

• global
• stability
• fractional
• nonlinear
• feedback
• positive
• system