LQR is a linear quadratic regulator whose object is a linear system given in the form of state space in modern control theory, and the objective function is a quadratic function of the object state and control input. The optimal solution of LQR can be written as a unified analytical expression and can lead to a simple state feedback control law. Linear quadratic control theory has become an important tool for feedback design systems. It is characterized by an effective analysis method for the design of multivariable feedback systems and it can be adapted to time-varying systems and generate disturbance signals and solve measuring noise problems and finally it can handle finite and infinite time intervals.