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Exotic Lyapunov Functionals for Boundedness and Stability

In: Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales

Author

Listed:
  • Murat Adıvar

    (Fayetteville State University, Broadwell College of Business and Economics)

  • Youssef N. Raffoul

    (University of Dayton, Department of Mathematics)

Abstract

Summary This chapter is devoted primarily to the construction of exotic Lyapunov functionals for the study of boundedness, stability and exponential stability. Necessary and sufficient conditions for scalar and vector Volterra integro-dynamic equations will be given via the use of Lyapunov functionals. It is pointed out that in the case of exponential stability, Lyapunov functionals are hard to extend to vector Volterra integro-dynamic equations Volterra integro-dynamic or to Volterra integro-dynamic equations with infinite delay Infinite delay . Most of the contents of this chapter are new and never been published elsewhere.

Suggested Citation

  • Murat Adıvar & Youssef N. Raffoul, 2020. "Exotic Lyapunov Functionals for Boundedness and Stability," Springer Books, in: Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales, chapter 0, pages 195-236, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-42117-5_5
    DOI: 10.1007/978-3-030-42117-5_5
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