We have a linear system $y\prime = A(t)y$, where $A(t)$ is continuous. How to prove that the stability of the zero solution implies that of every other solution of this system?
I know the common trick is, let $\phi(t)$ be the solution whose stability is to be tested, and consider another solution $y = \phi + z$, we have $z\prime = A(t)z$, and we know that $z =0$ is a stable solution for this system. But how to proceed to the conclusion that $\phi(t)$ is stable?
Thanks!