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Decay Rate Characterization for Positive Singular Systems with Unbounded Delays
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  • Bohao Zhu,
  • James Lam,
  • Yukang Cui,
  • Jason Ying Kuen Chan,
  • Ka-Wai Kwok
Bohao Zhu
The University of Hong Kong Department of Mechanical Engineering
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James Lam
The University of Hong Kong Department of Mechanical Engineering
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Yukang Cui
Shenzhen University College of Mechatronics and Control Engineering

Corresponding Author:cuiyukang@gmail.com

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Jason Ying Kuen Chan
The Chinese University of Hong Kong Department of Otorhinolaryngology Head and Neck Surgery
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Ka-Wai Kwok
The University of Hong Kong Department of Mechanical Engineering
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Abstract

This paper investigates the decay rates of continuous-time singular systems with unbounded delays. By introducing an auxiliary system for the original system, the positivity and asymptotic stability conditions of the system are investigated first. Then, µ-stability criteria, which are applied to characterize the decay rates of the systems, are proposed, and the relation between the system matrices and µ-stability is studied. Those results include the stability of positive singular systems with bounded time-varying delays and time-varying delays with linear growth rate as special cases. Finally, a numerical example is given to illustrate the obtained theoretical results.