Mixed H₂/H_∞ control for discrete-time systems via convex optimization

Abstract

A mixed 'lei.I 'lie,, problem for discrete-time systems is solved by converting it into a convex optimization problem over a finite-dimensional space.Key Words-Robust control; multiobjective control; convex programming.Abstract-A mixed 'le.ii :Jl"' control problem for discrete-time systems is considered, where an upper bound on the 'lei norm of a closed loop transfer matrix is minimized subject to an :Jl,,, 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 :Jl,,, controller. In particular, the state dimension of nearly optimal outputfeedback controllers need not exceed the plant dimension.

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