Two questions concerning the boundary control of certain elastic systems (Q1176517)

The author first considers conditions under which a system \[ \ddot x(t)+D\dot x(t)+Ax(t)=Cu(t),\quad u(t)=-K\dot x(t), \] with constant operators \(A\), \(C\), \(D\), \(K\), on a Hilbert space, has stable solutions \(x=x_ 0 e^{\lambda_ 0 t}\), \(\text{Re }\lambda_ 0<0\). Then he uses these results to analyze stability of three hyperbolic equations in a domain \(0<x<1\), \(t>0\), with the same boundary conditions \(w(0,t)=0\), \(w_ x(1,t)=-kW_ t(1,t)\), and another hyperbolic equation with delayed boundary conditions.