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Instability of discrete systems. (English) Zbl 0912.39005
Let $$x(t+1)= A(t)x(t)$$ be an unstable system. Criteria are given such that the zero solution of $$y(t+1) =A(t)+ f(t,y(t))$$, where $$f(t,0)=0$$, is also unstable or asymptotic unstable. The proofs use the method of discrete $$(h,k)$$-dichotomies.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A10 Additive difference equations
##### Keywords:
instability; discrete systems; discrete dichotomies
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