On the estimation of solution bounds of the generalized Lyapunov equationsand the robust root clustering for the linear perturbed systems

This paper measures the solution bounds for the generalized Lyapunov equati ons (GLE). By making use of linear algebraic techniques, we estimate the up per and lower matrix bounds for the solutions of the above equations. All t he proposed bounds are new, and it is also shown that the majority of exist ing bounds are the special cases of these results. Furthermore, according t o these bounds, the problem of robust root clustering in sub-regions of the complex plane for linear time-invariant systems subjected to parameter per turbations is solved. The tolerance perturbation bounds for robust clusteri ng in the given sub-regions are estimated. Compared to previous results, th e feature of these tolerance bounds is that they are independent of the sol ution of the GLE.