Abstract: It is inevitable to ignore some factors during modeling, and thus lead to some model errors.So designing controllers based on uncertain non-precise model is very important.With the efforts of researchers, online system H_∞ control has yield great achievement.However, it still has some problems, such as complex solving process, weak conservation, complex structures and high order controllers.The present study uses computational structural mechanics and optimal control theory to try to solve these problems.Induced norm is an eigenvalue problem in structural mechanics, i.e.elastic and stable Euler critical force or eigenvalue of structural vibration.Precise integration with extended Wittrick-Williams(W-W) algorithm is used to calculate induced norm by introducing the concept of interval mixed energy.And then this method is introduced to Market-Based Control theory and the MBC robust control for linear system is proposed.In the robust control, the stability and parameter identification are validated through Lyapunov direct method.Finally, a high controlled structure is simulated to compare the performance of the MBC robust control and the H_∞ robust algorithm.The results indicate that the induced norm cannot reach critical force, and otherwise the control input will be infinite.MBC robust control is better than H_∞ robust control algorithm, and has better strain capacity and shorter online calculation time.MBC robust control can be used in high or long-span structures.