The global (absolute) stability of nonlinear systems with negative
feedbacks and positive descriptor linear parts is addressed. Transfer
matrices of positive descriptor linear systems are analyzed. The
characteristics u = f(e) of the
nonlinear parts satisfy the condition
k₁e
≤ f(e) ≤ k₂e
for some positive k₁, k₂.
It is shown that the nonlinear feedback systems are globally
asymptotically stable if the Nyquist plots of the positive descriptor
linear parts are located in the right-hand side of the circles (–¹/k₁,
–¹/k₂).
The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.