The aim of designing a feedback controller is to stabilise the closed-loop dynamic behaviour and to make sure that it meets given performance requirements. The chapter introduces a number of stability notions such as Lyapunov stability, asymptotic stability, internal stability and input-output or bounded input-bounded output stability. For internal stability, all eigenvalues of the system matrix must have a negative real part. Especially for closed-loop MIMO systems, internal stability requires that for all initial conditions and all bounded signals injected at any place in the system, all states remain bounded for all future time. A linear MIMO system is input-output stable if and only if all poles of the transfer function matrix have a negative real part.