Abstract: This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l₂(Gl₂) and generalized H₂(GH₂) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl₂/GH₂control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

Key words: Mixed Gl₂/GH₂ synthesis, Multi-objective optimization, Robust control, Discrete linear time-invariant systems, G-shaping paradigm

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