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Lyapunov function of general Lurie systems with multiple nonlinearities. (English) Zbl 1051.93081

The authors study the absolute stability problem of general Lur’e control systems with multiple nonlinearities. Some new necessary and sufficient conditions are obtained for the existence of a Lyapunov function of extended Lur’e form with negative definite and negative semidefinite derivatives. From these conditions, some very general algebraic criteria for absolute stability are obtained, which extend and generalize previous works on the subject. A numerical example is presented to illustrate the effectiveness of the new criteria.

MSC:

93D10 Popov-type stability of feedback systems
93D30 Lyapunov and storage functions
93C10 Nonlinear systems in control theory
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