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).
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