Abstract: Optimal tracking performance for a class of uncertainty systems is discussed in the presence of control energy constraint under internal model control(IMC) structure.Firstly,an average performance index containing tracking error and control energy over a class of additive model errors is defined.Then,minimizing the performance by spectral factorization,we obtain an optimal controller design method,which can be used to take simultaneous account of model uncertainty and control energy constraint and evaluate optimal tracking performance and control energy in practical control system designs.