1988 Volume 1 Issue 1 Pages 9-16
This paper presents a robust stability condition for feedback systems in practice with uncertain nonlinearity. First, the boundedness of the “gain” for a nonlinear subsystem is discussed by means of some block diagram transformation. Secondly, a main theorem for L2-stability is derived using the small gain theorem and the input-output approach, after some considerations on the stability of the linearized nominal closed-loop system. This theorem is equivalent to the Popov criterion, but exhibits the stability margin explicitly. The relation between Aizerman's conjecture and this robust stability condition is also discussed. Then, a condition for the validity of Aizerman's conjecture is presented. Finally, typical examples including a counterexample to the conjecture are given to illustrate the results.