An explicit Formula for the suboptimal control of linear plants has been derived by Teodorescu (1985). Based on this result, the present paper proves that the suboptimal control and trajectory can be obtained by solving a matrix equation of the formXLX+XH+E= 0, whereL, H, Eare some constant, parameter-dependent matrices. The equation is easier to solve in comparison with the customary Riccati equation. An example is worked out to illustrate the steps of the procedure.