On stability of linear periodic differential difference equations

  • V.G. Kurbatov
  • V.I. Kuznetsova
Keywords: Stability, differential difference equation, functional differential equation, delay, causal invertibility, differential operator

Abstract

The paper considers the equation

∞                        

aj(t)x' (t - hj)o m(t,s)x' (t-s) ds

j=o

 

∞ 

+bj(t)x (t-hj)o n(t,s)x(t - s) ds = f(t)

j=o

where the operator-valued bounded functions aj and bj are 2π-periodic, and the operator-valued kernels m and n are 2π-periodic with respect to the first argument. The connection between the input-output stability of the equation and the invertibility of a family of operators acting on the space of periodic functions is investigated.

Keywords: Stability, differential difference equation, functional differential equation, delay, causal invertibility, differential operator

Published
2018-07-17
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606