Robust $D$ -Stability for a Class of Complex Singularly Perturbed Systems

This brief is concerned with the robust
D
-stability problem for a class of complex singularly perturbed systems with state delay. According to singular system approach, sufficient conditions, which are tested easily, are obtained by introduce delay-dependent state feedback, to ensure that the two-time-scale systems are regular, impulse free and
D
-stable, that is, all its poles are located with a specified disk for all small positive parameter epsiv isin (0,epsiv*) .