Stability and Boundedness of Solutions of LTV system

Question

I have the differential equation: $$\dot{x} = \Phi(x,t)[Ax+f(t)] $$ where: $$A \in R^{n\times n}- \ Hurwitz $$ $$ f(t) \in R^n \ and \ \Vert{f(t)\Vert < \infty}; $$ and $$ \Phi(x,t) = diag\{\frac{(e^{x_i}+1)^2}{e^{x_i}}\beta_i,\ \beta_i >0 ,\ i = 1..n\}=\begin{vmatrix}\frac{(e^{x_1}+1)^2}{e^{x_1}}\beta_1 & \cdots & 0 \\ \vdots &\frac{(e^{x_i}+1)^2}{e^{x_i}}\beta_i & \vdots \\ 0& \cdots & \frac{(e^{x_n}+1)^2}{e^{x_n}}\beta_n \\\end{vmatrix}$$ My question: How do i check if the solution of the equation is bounded and stable? Thank you!