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Positivity and Stability Analysis of Homogeneous Coupled Differential-difference Equations with Time-varying Delays

Journal Article


Abstract


  • This note studies the positivity and stability of homogeneous coupled differential-difference equations with time-varying delays. First, a sufficient positivity condition is proposed for the nonlinear coupled differential-difference equations with delays. Then, based on this positivity condition, we present necessary and sufficient conditions ensuring the exponential stability and bounding the decay rate for time-delay homogeneous coupled differential-difference equations with homogeneity of degree one. Furthermore, the necessary and sufficient condition is extended to the global polynomial stability analysis of homogeneous coupled differential-difference equations when the degree of homogeneity is greater than one and the decay rate is also investigated. Numerical examples are employed to show the effectiveness of the obtained results.

Publication Date


  • 2021

Citation


  • Cui, Y., Shen, J., Zhang, W., Feng, Z., & Gong, X. (2021). Positivity and Stability Analysis of Homogeneous Coupled Differential-difference Equations with Time-varying Delays. IEEE Transactions on Automatic Control. doi:10.1109/TAC.2021.3122380

Scopus Eid


  • 2-s2.0-85118538635

Web Of Science Accession Number


Abstract


  • This note studies the positivity and stability of homogeneous coupled differential-difference equations with time-varying delays. First, a sufficient positivity condition is proposed for the nonlinear coupled differential-difference equations with delays. Then, based on this positivity condition, we present necessary and sufficient conditions ensuring the exponential stability and bounding the decay rate for time-delay homogeneous coupled differential-difference equations with homogeneity of degree one. Furthermore, the necessary and sufficient condition is extended to the global polynomial stability analysis of homogeneous coupled differential-difference equations when the degree of homogeneity is greater than one and the decay rate is also investigated. Numerical examples are employed to show the effectiveness of the obtained results.

Publication Date


  • 2021

Citation


  • Cui, Y., Shen, J., Zhang, W., Feng, Z., & Gong, X. (2021). Positivity and Stability Analysis of Homogeneous Coupled Differential-difference Equations with Time-varying Delays. IEEE Transactions on Automatic Control. doi:10.1109/TAC.2021.3122380

Scopus Eid


  • 2-s2.0-85118538635

Web Of Science Accession Number