Stability Analysis of Linear Neutral Systems with Multiple Time Delays

Mathematical models with time delays are often encountered in various engineering systems due to measurement and computational delays, transmission and transport lags. Since the existence of time delays is frequently the source of instability, an important theme in neutral delay-differential systems is the stability of response characteristics. Different methods have been presented to deal with the stability problem of neutral systems with time delays in the literature. A number of stability criteria based on the characteristic equation approach, involving the determination of eigenvalues, measures and norms of matrices, or matrix conditions in terms of Hurwitz matrices, have been presented by Hale et al. [4], Li [9], Hu et al. [6], and Cao and He [1, 2]. Some stability criteria (delay-independent or delay-dependent) are given in terms of the Lyapunov function and matrix inequalities (see, e.g., Lien et al. [10], Fridman [3], and Niculescu [11]). Based on the linear matrix inequality (LMI) approach, robust stability conditions have been developed to make the criteria less conservative, see, for example, Park [12]. Recently, the study of stability has been extended to neutral systems with multiple time delays. Bymaking use of the characteristic equation of the system, Hui andHu [7] derived a delay-independent stability criterion in terms of the matrix measure and spectral norm of the matrix. In order to reduce the conservatism in the criterion of Hui and Hu [7], Won and Park [13] proposed a new delay-independent criterion in terms of the spectral radius of modulus matrices. However, we have found that a technical error, as shown in the next section, exists in the proof of the criterion of Won and Park [13]. This paper deals with the asymptotic stability of linear neutral systems with multiple time delays. Using the characteristic equation of the system, new delay-independent stability criteria are derived. Scalar inequalities involving the spectral radius and modulus