Abstract
This paper provides new insights into the currently available extended linear matrix inequality (LMI) conditions for control of discrete-time linear systems, motivating the use of two intrinsically different extended LMI characterizations for ℋ2 performance. While these conditions are equivalent for ℋ2 analysis and many ℋ2 control problems related to precisely known linear time-invariant (LTI) systems, they generally yield different results when employed for multi-objective ℋ2/ℋ∞ control and ℋ2 analysis and control of uncertain linear systems. The advantage of considering both the ℋ2 LMIs for robust ℋ2 state feedback and multi-objective ℋ2/ℋ∞ control design is demonstrated by means of exhaustive numerical comparisons.
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