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

This paper deals with the problem of the H-2/H-infinity control based on finite-time boundedness for linear stochastic systems. The motivation for investigating this problem comes from one observation that the H-2/H-infinity control does not involve systems' transient performance. To express this problem clearly, a concept called finite-time H-2/H-infinity control is introduced. Moreover, state feedback and observer-based finite-time H-2/H-infinity controllers are designed, which guarantee finite-time boundedness, H-2 performance index, and H-2/H-infinity performance index of the closed-loop systems. Furthermore, an optimization algorithm on the finite-time H-2/H-infinity control is presented to obtain the minimum values of the H(2 )index and H-infinity index. Finally, we use an example to show the validity of the obtained results.