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This paper delves into the positive realness corresponding to singular fractional order systems with fractional order \(0<\alpha <1\) and \(1<\alpha <2\) . With the aid of the Kalman-Yakubovich-Popov (KYP) lemma, novel conditions for the positive realness for singular fractional order systems are obtained with regard to linear matrix inequalities. The new methods eliminate the previous requirement of equality constraints in existing results. Therefore, computations are further simplified, for results can be calculated directly by applying LMI tools in Matlab. Additionally, numerical simulations are exhibited to substantiate the reliability and practicality of the methods proposed in this work.

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Positive Real Lemmas for Singular Fractional Order Systems Without Equality Constraints

  • 会议论文

  • 发表日期：

    2025年

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  • Yihui Zhu,
  • Rui Chen,
  • Shiqin Xiao,
  • Dingkai Weng,
  • Yiheng Wei

摘要

This paper delves into the positive realness corresponding to singular fractional order systems with fractional order \(0<\alpha <1\) and \(1<\alpha <2\) . With the aid of the Kalman-Yakubovich-Popov (KYP) lemma, novel conditions for the positive realness for singular fractional order systems are obtained with regard to linear matrix inequalities. The new methods eliminate the previous requirement of equality constraints in existing results. Therefore, computations are further simplified, for results can be calculated directly by applying LMI tools in Matlab. Additionally, numerical simulations are exhibited to substantiate the reliability and practicality of the methods proposed in this work.