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Cui, Yukang; Feng, Zhiguang; Shen, Jun; Chen, Yong

\(L_\infty\)-gain analysis for positive singular time-delay systems. (English) Zbl 1395.93244

J. Franklin Inst. 354, No. 13, 5162-5175 (2017).
Summary: This paper is devoted to the characterization of \(L_\infty\)-gain for positive singular systems with time-varying delays. First, we introduce an augmented system to replace the original system in order to analyze the positivity of singular systems with time-varying delays. By investigating the monotonicity of state trajectory, the \(L_\infty\)-gain for singular system with constant delays is characterized. Then, by comparing the trajectories of time-varying delay system and constant delay case, we finally propose the \(L_\infty\)-gain for singular system with time-varying delays. It is shown that the \(L_\infty\)-gain of positive singular systems is independent of the magnitude of delays.

Cited in 12 Documents

MSC:

93C05 Linear systems in control theory
93D20 Asymptotic stability in control theory
93C15 Control/observation systems governed by ordinary differential equations

Keywords:

\(l_\infty\)-gain; positive singular time-delay systems
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References:

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