A note on stability of functional difference equations

In this note, we consider perturbed linear functional difference equations with discrete and distributed delays which play a fundamental role in several stability and stabilizability problems of time-delay systems. Linear and nonlinear perturbations are considered. Sufficient conditions for exponential stability of the perturbed solutions are given.

[1]  Pierdomenico Pepe,et al.  Direct and converse Lyapunov theorems for functional difference systems , 2014, Autom..

[2]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[3]  Daniel Melchor-Aguilar,et al.  Exponential stability of linear continuous time difference systems with multiple delays , 2013, Syst. Control. Lett..

[4]  Daniel Melchor-Aguilar.  Further results on exponential stability of linear continuous time difference systems , 2013, Appl. Math. Comput..

[6]  Erik I. Verriest.  New qualitative methods for stability of delay systems , 2001, Kybernetika.

[7]  Rogelio Lozano,et al.  Stability conditions for integral delay systems , 2010 .

[8]  Pierdomenico Pepe,et al.  The Liapunov's second method for continuous time difference equations , 2003 .

[9]  Luis Carvalho.  On quadratic Liapunov functionals for linear difference equations , 1996 .

[10]  Richard Bellman,et al.  Differential-Difference Equations , 1967 .

[11]  S. Cheng,et al.  Solution Estimates for Semilinear Difference-Delay Equations with Continuous Time , 2007 .

[12]  Daniel Alejandro Melchor-Aguilar.  Exponential stability of some linear continuous time difference systems , 2012, Syst. Control. Lett..

[13]  Daniel Alejandro Melchor-Aguilar,et al.  On stability of integral delay systems , 2010, Appl. Math. Comput..

[14]  M. Krstić.  Delay Compensation for Nonlinear, Adaptive, and PDE Systems , 2009 .

[15]  Iasson Karafyllis,et al.  On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations , 2013, ArXiv.

[16]  Leonid E. Shaikhet.  About Lyapunov functionals construction for difference equations with continuous time , 2004, Appl. Math. Lett..

[17]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.