In this paper we discuss the issue of optimal control of piecewise affine systems based on discontinuous quadratic Lyapunov function, given the stability of the said system, first we calculate the upper bound of the cost function, then we consider the control input as the state feedback and finally, by minimizing the upper bound of the cost function, the state feedback coefficients are calculated. Note that if we minimize upper bound the cost function is minimized. It is worth noting that the optimization problem is turned into a semidefinite programming problem with bilinear constraints. These problems can be solved using numerical or any other methods. Finally, to check the effectiveness of the method, we have listed a numerical example.

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