Abstract: One purpose of this work is to establish the nominal description of mixed H₂/l₁ optimization problems evolving from mixed H₂/l₁ control problems for SISO discrete time systems. Some assumptions on mixed H₂/l₁ optimization problems are made. Another purpose of this work is to study the structure of the closure of feasible region for mixed H₂/l₁ optimization problems. The feasible region is the set of a map of a free parameter which is rational stable and satisfies some constraints. It is shown that the closure is exactly the set of the same map, where the free parameter is stable and satisfies the same constraints. It is convenient to describe mixed H₂/l₁ optimization problems with a stable free parameter. For mixed H₂/l₁ optimization problems with stable free parameter, the existence and uniqueness of the solution can be easily obtained.

Key words: l₁ control, H₂ control, discrete time systems, closure

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