The final chapter summarises the unified framework of control and detection. The Bezout identity is the mathematical basis for the parameterisation of all stabilising controllers and stability analysis of feedback control systems and thus crucial for controller synthesis and robustness analysis. More importantly, it models a mapping from the system input-output signals to the residual signals. The Bezout identity and its variations are summarised as the core of the unified framework. It is followed by the introduction of SIR and SKR representations and the associated image, kernel, and residual subspaces or manifolds. The chapter concludes by revisiting the foundational theoretical tools: normalised coprime factorisations, projection methods, and Hamiltonian systems.