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Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance

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  • Xingao Zhu
  • Yuangong Sun

Abstract

Reachable set bounding for homogeneous nonlinear systems with delay and disturbance is studied. By the usage of a new method for stability analysis of positive systems, an explicit necessary and sufficient condition is first derived to guarantee that all the states of positive homogeneous time-delay systems with degree converge asymptotically within a specific ball. Furthermore, the main result is extended to a class of nonlinear time variant systems. A numerical example is given to demonstrate the effectiveness of the obtained results.

Suggested Citation

  • Xingao Zhu & Yuangong Sun, 2019. "Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance," Complexity, Hindawi, vol. 2019, pages 1-6, July.
    • Handle: RePEc:hin:complx:8698294
    DOI: 10.1155/2019/8698294
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    References listed on IDEAS

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    1. Li, Yanan & Sun, Yuangong & Meng, Fanwei & Tian, Yazhou, 2018. "Exponential stabilization of switched time-varying systems with delays and disturbances," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 131-140.
    2. P. T. Nam & P. N. Pathirana & H. Trinh, 2013. "Exponential Convergence of Time-Delay Systems in the Presence of Bounded Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 843-852, June.
    3. Shao, Jing & Meng, Fanwei & Zheng, Zhaowen, 2015. "Oscillation theorems for linear matrix Hamiltonian systems," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 402-409.
    4. Nguyen D. That & Phan T. Nam & Q. P. Ha, 2013. "Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 96-107, April.
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