On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems CHIEN-HUA LEE{ and SU-TSUNG LEE{This paper measures the solution bounds for the generalized Lyapunov equations (GLE). By making use of linear algebraic techniques, we estimate the upper and lower matrix bounds for the solutions of the above equations. All the proposed bounds are new, and it is also shown that the majority of existing bounds are the special cases of these results. Furthermore, according to these bounds, the problem of robust root clustering in sub-regions of the complex plane for linear time-invariant systems subjected to parameter perturbations is solved. The tolerance perturbation bounds for robust clustering in the given sub-regions are estimated. Compared to previous results, the feature of these tolerance bounds is that they are independent of the solution of the GLE.