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This paper deals with the problem of the H2/H∞ control based on finite-time boundedness for linear stochastic systems. The motivation for investigating this problem comes from one observation that the H2/H∞ control does not involve systems’ transient performance. To express this problem clearly, a concept called finite-time H2/H∞ control is introduced. Moreover, state feedback and observer-based finite-time H2/H∞ controllers are designed, which guarantee finite-time boundedness, H2 performance index, and H∞ performance index of the closed-loop systems. Furthermore, an optimization algorithm on the finite-time H2/H∞ control is presented to obtain the minimum values of the H2 index and H∞ index. Finally, we use an example to show the validity of the obtained results.

Finite-Time H2/H∞ Control for Linear Itô Stochastic Systems with x,u,v-Dependent Noise