Abstract
In this paper, necessary and sufficient conditions are obtained for the existence of Lyapunov functional of extended Lur'e form to guarantee absolute stability for multiple delay general Lur'e control systems with multiple nonlinearities, and the existence reduces to a problem of solving a group of linear matrix inequalities (LMIs). When the LMIs are feasible, the free parameters in the Lyapunov functional are given by the solution of these LMIs. Otherwise, this class of Lyapunov functional does not exist.
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