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 for the asymptotic stability of the original system. Furthermore, a simple estimate of an upper bound of singular perturbation parameter ε is proposed so that the original system is asymptotically stable for any Two numerical examples are provided to illustrate the use of our main results.
Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division February 13, 2004. Associate Editor: N. Olgac.
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Pan, S., Chen, C., and Hsieh, J. (December 3, 2004). "Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays ." ASME. J. Dyn. Sys., Meas., Control. September 2004; 126(3): 462–466. https://doi.org/10.1115/1.1793172
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