The continuous-time generalized predictive control (CGPC) using a long horizon cost function has superior robustness as compared to several other control strategies suitable for adaptive control. The main purpose of this paper is to put forward an analytical, explicit stable CGPC control design method for minimum-phase SISO systems that is based on a set of closed-loop characteristics with definite time-domain specifications. Explicit formulae for closed-loop characteristic polynomials are given and then the prototype design characteristic polynomials are catalogued that can serve as a basis for fully analytical design procedure assuring both the nominal stability and nominal performance specifications. A numerical example is given in order to illustrate the approach.