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Stability and Boundedness

  • Youssef N. Raffoul
Chapter

Abstract

In this chapter we provide a brief introduction to difference calculus including basic material on Volterra difference equations. Using the z-transform we state some known theorems regarding stability of the zero solution of Volterra difference equations of convolution types. We move on to introducing Lyapunov functions for autonomous difference equations and state some known results concerning stability and boundedness. In Section 1.3 we introduce the concept of total stability and its correlation with uniform asymptotic stability for perturbed Volterra difference equations.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Youssef N. Raffoul
    • 1
  1. 1.Department of MathematicsUniversity of DaytonDaytonUSA

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