Mixed [formula omitted] control for discrete-time systems via convex optimization

Abstract

A mixed H 2 H ∞ control problem for discrete-time systems is considered, where an upper bound on the H 2 norm of a closed loop transfer matrix is minimized subject to an H ∞ constraint on another closed loop transfer 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 H ∞ controller. In particular, the state dimension of nearly optimal output-feedback controllers need not exceed the plant dimension.