This work aims at the investigation of stability and robustness of the optimal control problems. A one dimensional harmonic oscillator is considered in order to get insight about such problems. The stability of the solutions to the optimal control problem of the system is investigated by the stability operator which is constructed as the kernel operator of quadratic form coming from the second variation of the cost functional evaluated at the optimal solution. The stability operator appears as an integral operator, and its spectrum determines the robustness. Depending on the structure of the model under consideration investigations may not be analytical. Time varies between 0 and T inclusive. By scaling the time variable to the interval [0, 1] and considering all temporal entities bivariate functions of t and T, it is possible to develop a perturbative series. This is called an instantenous expansion somehow. Here this approach is used to approximate stability solutions. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim.