Previous studies have shown that a controllable linear system can be driven from a given initial condition to a desired target by means of a polynomial input function whose coefficients are obtained simply by solving a set of linear algebraic equations. This paper shows how the application of the concept of polynomial controllability is useful for solving a suboptimal control problem. In particular we present a simple procedure for searching for a control function that minimizes a quadratic performance measure while the system is transferring between specified end-points. The approach is implemented for both state-space and singular linear time-invariant controllable systems.