The class of systems considered is of the type \[ (Gw)(t) =\int^t_{-\infty} g(t, \tau) w(\tau) d\tau, \] including systems of the form \(x'= A(t)x +B(t)w\), \(z= C(t)x\), with \(A\) defining an uniformly exponentially stable evolution. The entropy denoted \(E(G,\gamma,t)\) is defined starting from a spectral factorization of \(I-\gamma^{-2} G*G=M*M\) as \[ E(G, \gamma, t) =\lim_{\alpha \to 0} \left(- {\gamma^2 \over 2^\alpha} \ln\text{det} \bigl((\widehat m(t)+ \alpha m(t,t) \bigr)^T \bigl(\widehat m(t)+ \alpha m(t,t) \bigr) \right), \] where \(\widehat m\) and \(m\) appear in the representation \[ (Mw)(t) =\widehat m(t) w(t)+ \int^t_{-\infty} m(t,\tau) w(\tau) d \tau. \] If the system is given by the state-space realization, then \(E(G, \gamma,t) =\text{trace} (B(t)^T X(t)B(t))\), where \(X\) is the positive semidefinite stabilizing solution to the Riccati equation: \[ X'+ A^TX +XA +\gamma^{-2} XBB^TX +C^T C=0. \] The significant titles of sections are: The Relationship with discrete-time entropy, The entropy of linear time-invariant systems, Relationship between the entropy and the \(H_\infty\)-norm, relationship between the entropy and the \(H_2\) norm, Minimum entropy control.