| H2 control and H_∞ control occupy the most significant status inthe modern control theory. They have been received comprehensive attentions in many fields, and some research results have been acquired. As a kind of multitarget control problems, mixed H2/H_∞ control problempresented in the late eighties of the 20th century integrates H2 performance design with H_∞' s, then the whole system can not only attainan excellent regulative performance, but also keep the robust stability. On the other hand, variable structure control (VSC) got researchers' attentions because of its absolute robustness for the parameter uncertainty and the exterior disturbances on the sliding mode. The research fields of VSC also embrace aerocraft control robot control electric & electrician system control, etc.This paper integrated mixed H2/H_∞ optimization with VSC, makinguse of VSC invariability, so that the system could achieve mixed optimization between robust performance and the dynamic and stable performance in the sliding mode, then the concept of variable structure control based on mixed H2/H_∞ optimization was presented. Afterintroducing the methods of states transformation and the disturbance redefinition, this paper described the system' s dynamics equation on the sliding mode. By means of defining the assistant controlled signals, this paper gained the generalized plant, and then made certain the terminal sliding mode' s expression through solving the mixed H2/H_∞optimization controller by way of using the convex approach based on state feedback. Last, the control law, which ensured the existence of sliding mode, was given and the stability was proved. The simulation results for a class of linear uncertainty systems with mismatching disturbance show the effective of this method. Not only have good dynamic and stable performance but also without loss robustness, the approach proposed in this paper should have preferable application foreground in the engineering fields.
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