An example of a linear discrete system with unstable Lyapunov exponents

We consider a discrete time-varying linear system
\begin{equation} x(m+1)=A(m)x(m),\quad m\in\mathbb Z,\quad x\in\mathbb R^n, \tag{1} \end{equation}
where $A(\cdot)$ is completely bounded on $\mathbb N$, i.e., $\sup_{m\in\mathbb N}\bigl(\|A(m)\|+\|A^{-1}(m)\|\bigr)<\infty$. Let $\lambda_1(A)\le\ldots\le\lambda_n(A)$ be the Lyapunov spectrum of the system (1). It is called stable if for any $\varepsilon>0$ there exists a $\delta>0$ such that for every completely bounded $n\times n$-matrix $R(\cdot)$, $\sup_{m\in\mathbb N}\|R(m)-E\|<\delta$, the inequality
$$\max_{j=1,\ldots,n}|\lambda_j(A)-\lambda_j(AR)|<\varepsilon $$
holds. We construct an example of the system (1) with unstable Lyapunov spectrum.