This paper deals with delay Lurie-type neutral control system. Applying Lyapunov method, a new criterion based on linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds on delays and the free weighting matrices. Since the criterion takes the size of the neutral and discrete delays into account, it is less conservative than the existing ones. An example is shown that the result obtained by this new criterion not only significantly improves the existing results in the literature but also illustrates the reciprocal influences between the neutral and discrete delays.
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