Addresses less conservative control design for multiple design specifications. Although problems are described by a set of LMIs (linear matrix inequalities), they are solved with non-common LMI solutions to reduce the conservatism arising from seeking a common LMI solution. Noticing that completing the square can split two variables in BMI (bilinear matrix inequality) terms into two different LMI ones, we propose iterative algorithms while replacing non-positive quadratic terms by their upper bounds. A suitable choice of the parameters in these upper bounds guarantees the convergence property. An example is included.
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