---

In this research, an innovative numerical simulating approach for time domain analysis of multi degrees of freedom structures with uncertainty in dynamic properties is presented. A full scale finite element model of multi-story and multi bays of three sample structures has been constructed. The reduced order model of structure with holding the dominant and effective Gramians in the balanced state-space realization has been achieved for easy and safe design of the optimal control forces applied to the structure. Some easy selective control algorithms based on the Optimal-Stochastic control theories such as LQG, DLQRY and modified sliding mode control has been programmed with the simulation control sequences. Some real features of accurate control system such as time delay and noise signals in earthquake time histories and also measurement sensors are considered in illustrative simulation models. These models can be analyzed under either various intensity of corresponding earthquakes or desired random excitations passed through the suitable filters providing stochastic parameters of earthquake disturbances. This control procedure will be shown to be very efficient suppressing all the severities and difficulties may arise in design of a multi-objective optimal control system. The obtained results illustrate the feasibility and applicability of the proposed stochastic optimal control design of active control force providing a stable and energy-saving control strategy for tall building structures.