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In order to solve the problem that the cost of operation and erection of distributed cloud energy storage system in smart microgrid is high and it is difficult to find an effective overall control law, an observer-based controller design method is introduced to deal with a class of piecewise energy storage system with norm-bounded time-varying parameter uncertainties. By using the piecewise-affine singular Lyapunov functions combined with Projection lemma and some basic lemmas, an approach of designing observer-based robust feedback controller is given, the conclusions ensure the system possessing performance. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by scalar variables. We get the feedback controller gain and observer-based controller gain which can ensure the stability of systems, but also guarantee the performance of the piecewise-affine singular systems. The numerical simulation results show that the interference rejection is 6.5896. By comparing the cloud energy storage power supply system with the traditional power system, the effectiveness of the proposed design method is verified and the superiority of the method is also verified.