The authors develop further classical \(H_\infty\) feedback control theory with origins going back to the Nehari problem of left-coprime factorization of transfer functions. Stabilizability of the system is a necessary and sufficient condition for existence of such a factorization. The authors start with the bounded linear system denoted by \(\Sigma(A,B,C,D)\) given by \[ dz/dt= Az(t)+ Bu(t),\quad y(t)= Cz(t)+ Dz(t),\quad z(0)= z_0, \] with \(z\in Z\) (a Hilbert space), \(A\) generates a \(C_0\) semigroup \(T(t)\) in \(Z\). It is strongly stable if \(\lim T(t)= 0\), as \(t\to\infty\). It is exponentially stable if \(L^2\) inputs lead to a bounded state and \(L^2\) output. In the present paper, the authors consider state-space systems that are neither exponentially stable, nor detectable. Thus, much of the existing theory is not applicable. However, their systems are dissipative with collocated actuators and sensors (the word collocated describes the condition \(B= C^*\), which physically implies that actuators and sensors are placed in the same locations). The bounded linear system \(\Sigma(A,B,C,D)\) is statically stable if there exists a linear map \(K\) such that \(\Sigma(A_K,B,C,D)\) is strongly stable and bounded. \(A_K\) stands for \(A+ BKC\). The authors have shown in a previous paper that static stabilizability implies both strong stabilizability and strong detectability and in fact the whole closed loop system is stabilized. The robust stabilization problem is formulated in the frequency domain, as is the common practice. The example of the Euler-Bernoulli beam is given to illustrate this class of control problems. The authors proceed to give a quick outline of coprime factorization ideas. Let \(G(s)\) be a transfer function operator. (All operators listed here are \(H_\infty\).) Suppose that there exist operators \(N\), \(M\), \(X\), \(Y\), such that \(G(s)= M(s)^{-1}N(s)\) and \(MX\)-\(NY= I\), then \(M^{-1}N\) is called the left coprime factorization of \(G\). This is written as a matrix with operator entries. Using these operators and their Hermitian transposes, the authors proceed to define right coprime factorization and doubly coprime factorization. The corresponding equations are the Bézout equations. The authors introduce the following Riccati equation \[ A^* Qz+ QAz- (B^* Q+ NC)^* R^{-1}_1 (B^*Q+ NC)z+ C^* R_2Cz= 0. \] The operator \(Q\) is a strongly stabilizing solution to this Riccati equation. After some algebra, the authors offer existence arguments for strongly stabilizing solutions of their Riccati system. A theorem on maximal robustness margin for the stabilization of \(G\) follows from these algebraic manipulations. Finally, they offer a prescription for static stabilization. The authors comment their results may be surprizing to mathematicians working with hyperbolic partial differential equations. This paper is a continuation of outstanding past research of R. F. Curtain and her collaborators on linear feedback closed loop theories.