ABSTRACT. This paper considers control synthesis for polynomial control systems. The developed method leans upon Lyapunov stability and Bernstein certificates of positivity. We strive to develop an algorithm that computes a polynomial control and a polynomial Lyaponov function in the simplicial Bernstein form. Subsequently, we reduce the control synthesis problem to a finite number of evaluations of a polynomial within Bernstein coefficient bounds representing controls and Lyapunov functions. As a consequence, the equilibrium is asymptotically stable with this control.