Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays

The paper is to investigate the asymptotic stability for a general class of linear time-invariant singularly perturbed systems with multiple non-commensurate time delays. It is a common practice to investigate the asymptotic stability of the original system by establishing that of its slow subsystem and fast subsystem. A frequency-domain approach is first presented to determine a sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model), which is a singular system with multiple time delays, and the fast subsystem. Two delay-dependent criteria, ε-dependent and ε-independent, are then proposed in terms of the $H∞-norm$ for the asymptotic stability of the original system. Furthermore, a simple estimate of an upper bound $ε*$ of singular perturbation parameter ε is proposed so that the original system is asymptotically stable for any $ε∈0,ε*.$ Two numerical examples are provided to illustrate the use of our main results.