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Mixed \({\mathcal H}_ 2/{\mathcal H}_{\infty}\) control for discrete-time systems via convex optimization. (English) Zbl 0772.93055
Summary: A mixed \({\mathcal H}_ 2/{\mathcal H}_ \infty\) control problem for discrete- time systems is considered, where an upper bound on the \({\mathcal H}_ 2\) norm of a closed loop transfer matrix is minimized subject to an \({\mathcal H}_ \infty\) constraint on another closed loop matrix. Both state- feedback and output-feedback cases are considered. It is shown that these problems are equivalent to finite-dimensional convex programming problems. In the state-feedback case, nearly optimal controllers can be chosen to be static gains. In the output feedback case, nearly optimal controllers can be chosen to have a structure similar to that of the central single objective \({\mathcal H}_ \infty\) controller. In particular, the state dimension of nearly optimal output-feedback controllers need not exceed the plant dimension.

MSC:
93C55 Discrete-time control/observation systems
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