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Hyers–Ulam Stability, Exponential Stability, and Relative Controllability of Non‐Singular Delay Difference Equations

Author

Listed:
  • Sawitree Moonsuwan
  • Gul Rahmat
  • Atta Ullah
  • Muhammad Yasin Khan
  • Kamran
  • Kamal Shah

Abstract

In this paper, we study the uniqueness and existence of the solutions of four types of non‐singular delay difference equations by using the Banach contraction principles, fixed point theory, and Gronwall’s inequality. Furthermore, we discussed the Hyers–Ulam stability of all the given systems over bounded and unbounded discrete intervals. The exponential stability and controllability of some of the given systems are also characterized in terms of spectrum of a matrix concerning the system. The spectrum of a matrix can be easily obtained and can help us to characterize different types of stabilities of the given systems. At the end, few examples are provided to illustrate the theoretical results.

Suggested Citation

  • Sawitree Moonsuwan & Gul Rahmat & Atta Ullah & Muhammad Yasin Khan & Kamran & Kamal Shah, 2022. "Hyers–Ulam Stability, Exponential Stability, and Relative Controllability of Non‐Singular Delay Difference Equations," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:8911621
    DOI: 10.1155/2022/8911621
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    References listed on IDEAS

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    1. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Aftab Khan & Gul Rahmat & Akbar Zada, 2013. "On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups," International Journal of Differential Equations, Hindawi, vol. 2013, pages 1-4, July.
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