Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with application to Static Output Feedback

In this paper, we are interested in optimization problems arising in static output feedback controller design for a linear, time-invariant system of the form:         y Cx D w z C x D w D u x Ax B w Bu 21 1 11 12 1 = =  = where n xR is state vector, w n wR is the performance input, u n uR is input vector, z n zR is the performance output, y n yR is physical output vector, n n A  R is state matrix, u n n B  R is input matrix and n y n C  R is the output matrix.