Robust admissibility of time-varying singular systems with commensurate time delays

This paper addresses the problem of admissibility of time-varying singular systems with commensurate time delays. By introducing a new method to study the convergence of the fast sub-system, an admissibility condition is obtained in terms of linear matrix inequalities, which guarantees the considered time-varying singular delay system to be regular, impulse free and stable. Furthermore, a robust admissibility condition is proposed for the case when the time-varying system matrices admit the usual constant-plus-norm-bounded structure. It is theoretically established that the proposed robust admissibility condition is less conservative than the existing one in the literature. One of the important features of the results is that the inferred admissibility condition coincides with the usual stability condition for state-space delay systems. Moreover, the results are also applicable to the multiple rational delay case.