## Instability of discrete systems

### Summary

Summary: In this paper, we give criteria for instability and asymptotic instability for the null solution to the non-autonomous system of difference equations $y(t+1)=A(t)y(t) + f(t,y(t)), f(t,0)=0$, when the system $x(t+1)$=(t)$x(t)$ is unstable. In particular for A constant, we study instability from a new point of view. Our results are obtained using the method of discrete dichotomies, and cover a class of difference systems for which instability properties cannot be deduced from the classical results by Perron and Coppel.

39A11, 39A10

### Keywords/Phrases

instability, Perron's theorem, discrete dichotomies