Finite-time \(H_2/H_\infty\) control for linear Itô stochastic systems with \((x,u,v)\)-dependent noise
Summary: This paper deals with the problem of the \(H_2/H_\infty\) control based on finite-time boundedness for linear stochastic systems. The motivation for investigating this problem comes from one observation that the \(H_2/H_\infty\) control does not involve systems' transient performance. To express this problem clearly, a concept called finite-time \(H_2/H_\infty\) control is introduced. Moreover, state feedback and observer-based finite-time \(H_2/H_\infty\) controllers are designed, which guarantee finite-time boundedness, \(H_2\) performance index, and \(H_\infty\) performance index of the closed-loop systems. Furthermore, an optimization algorithm on the finite-time \(H_2/H_\infty\) control is presented to obtain the minimum values of the \(H_2\) index and \(H_\infty\) index. Finally, we use an example to show the validity of the obtained results.
scientific article; zbMATH DE number 7024883
scientific article