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Abstract: When a time-delay system involves multiple imaginary roots (MIRs), the stability analysis will become much more complicated than that in the case with only simple imaginary roots (SIRs). An MIR may exhibit different splitting behaviors and, to the best of the authors’ knowledge, their properties have not been fully investigated. In this paper, we focus on characterizing the invariance properties for MIRs with any multiplicity. Furthermore, the proposed methodology makes it possible to also cover some degenerate cases already encountered and discussed in the literature. In addition, we propose an easily implemented frequency-sweeping method, making it possible to derive the asymptotic behavior without invoking the Puiseux series. [Copyright &y& Elsevier]

Abstract: The stability of neutral systems with mixed delays is studied in this paper. A new discretized Lyapunov functional method is proposed. The method in this paper is less conservative than the existing ones and the results are very close to the analytical results. In addition, this method allows the coefficient matrix of the neutral term to have time-varying uncertainties. [Copyright &y& Elsevier]