The asymptomatic stability problem of robust with time lag is widely existed in active vibration isolation system. The influence of time lag on the optimal control algorithm is studied in this paper. And by utilizing LMI tools in MATLAB, variable step method is introduced to get the maximum allowable upper bound of the robust time lag in the optimal control system. Numerical simulation results verified the theory and contributed to the conclusion that with time lag increasing, the effect of controlling will become worse ,once the time lag exceed the maximum allowable delay boundary, the system will diverge.At the same time ,the upper bound can be improved by increasing feedback control and decreasing the corresponding weight of the control goals weighting matrix. The work of this paper is beneficial for the relevant experimental design.
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