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An optimization problem with robust and average constraints is introduced, where the constraints are described as parameter-dependent linear matrix inequalities. The difficulty of the parameter dependency is solved by using the scenario approach which employs random samples of the parameter. An explicit number of random samples such that the optimal solution of the scenario problem achieves prescribed accuracy and confidence is derived, which is the main result of this paper. It is then applied to an average pole placement problem with robust stability, and a numerical example is provided.

A Scenario Approach to Optimization Subject to Robust and Average LMIs