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A Calculation Method of Parameter-dependent LMIs on Bernstein Polynomial Basis: Polytopic Representation Case

A calculation method of polynomially parameter-dependent LMIs (Linear Matrix Inequalities) is proposed for the polytopic representation case. Employing multivariate Bernstein polynomial basis, the parameter-dependent LMI conditions are systematically transformed to standard LMIs, and it is shown that the finite division of the parameter region enables to reduce the conservativeness by the 2nd order of the division width. The features of the proposed calculation method are illustrated with numerical examples.