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In this paper, a new stability criterion for a class of neutral systems with multiple discrete and distributed time delays is provided. Based on the Lyapunov second method, a new delay-dependent stability criterion in terms of linear matrix inequality (LMI) is derived. Numerical examples are given to illustrate that the proposed result is less conservative. Introduction Delay is a kind of widespread physical phenomena in the nature [1-3]. Research of neutral delay system is controlled in recent decades the rise in the field of a hot spot, and is becoming more and more attention by people, such a time-delay systems not only contains the last motion, motion differential information also includes the past, this kind of neutral differential equation system can be used to describe the [1-6]. In the literature [6-9], some time-delay independent stability criteria were proposed. Literature [10-13] proposed the sufficient criterion of time-delay correlation stability by using the conversion method. In the literature [14], the variable delay neutral system was studied, but the stability criterion given by the literature was conservative. This paper presents delay-dependent criteria in the form of linear matrix inequality (LMI) based on Lyapunov second method. The paper compares the numerical examples with the existing ones, and illustrate the advantages of the conclusions obtained in this paper. Before giving the main theorem of this chapter, the following lemmas are given. Lemma 1: ( Park P. [11] ) Assume that for all given    , there are x n R a  ) ( and y n R b  ) ( . For any positive definite matrix r x n n R N   and matrix y r n n R M   , Satisfies the following matrix inequality:          d ) ( ) ( ) ( ) ( d ) ( ) ( 2 T T T                         b a N M NM N b a a b (1) Here,  represents ) ( ) ( 1 T I NM N I N M    . Lemma 2 [15] : For arbitrary constant matrices n n R M   , 0 T   M M , scalar 0   and Vector function m R  ] , 0 [ :   , satisfying (2):                    0 0 0 ) ) ( ( ) ) ( ( ) ( ) ( d M d d M T T (2) Based on the above lemma, the main conclusions of this paper are given below. Stability Theorem Consider the following neutral system(3a) with time delay.              m

Delay-dependent Stability Criterion for a Class of Neutral Systems with Multiple Mixed Delays