Admissibility criteria for a class of nonlinear singular systems with an interval time-varying delay

This paper investigates the admissibility analysis problem for a class of nonlinear singular systems with an interval time-varying delay. A delay-range-dependent and delay-rate-independent admissibility criterion for nonlinear singular time-delay system is first established. Furthermore, it is shown that the admissibility criterion proposed in this paper is more simple and less conservative than one in [Nonlinear Analysis: Real World Appl., 2011, 12: 1152-1162]. Then, a pair of admissibility criteria for linear singular systems with a constant and time-varying delay are given, respectively. All admissibility criteria are given in the form of simple linear matrix inequalities, which can be easily solved by the YALMIP toolbox of MATLAB. Finally, three numerical examples are given to illustrate the effectiveness of the theoretical method.