Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Robust Stability of Feedback Control Systems Containing an Uncertain Nonlinearity
Yoshifumi OKUYAMA
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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.

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