Power system stability means the ability to develop restoring forces equal to or greater than the disturbing forces to maintain the state of equilibrium. Successful operation of a power system depends largely on providing reliable and uninterrupted service to the loads by the power utility. The stability of the power system is concerned with the behavior of the synchronous machines after they have been disturbed. If the disturbance does not involve any net change in power, the machines should return to their original state. Due to small disturbances, power system experience these poorly damped low frequency oscillations. The dynamic stability of power systems are also affected by these low frequency oscillations. This paper presents to analyze and obtain the optimum gain for damping oscillation in SMIB by using Riccati matrix method to improve dynamic power system stability. The result shows that with suitable gain which is act as a stabilizer that taken from Riccati matrix, the oscillations of rotor speed and rotor angle can be well damped and hence the system stability is enhanced.