Global Stability of Nonlinear Feedback Systems with Positive Linear Parts

Abstract

Abstract The global (absolute) stability of nonlinear systems with negative feedbacks and positive not necessary asymptotically stable linear parts is addressed. The characteristics u = f ( e ) u = f(e) of the nonlinear parts satisfy the condition k 1 e ≤ f ( e ) ≤ k 2 e {k_1}e \le f(e) \le {k_2}e for some positive k 1 {k_1} , k 2 {k_2} . It is shown that the nonlinear systems are globally asymptotically stable if the Nyquist plots of the positive linear parts are located in the right-hand side of the circles − 1 k 1 , − 1 k 2 \left( { - {1 \over {{k_1}}}, - {1 \over {{k_2}}}} \right) .