A necessary and sufficient condition for static output feedback (SOF) controller design for linear systems with polytopic uncertainties is derived in the form of the linear matrix inequalities (LMIs) with a line search over some scalar parameters to locate the closed-loop poles in the desired complex plane. The extension of the result to H2 SOF synthesis is studied, which guarantees a minimum bound on the H2 performance level in addition to the pole placement constraints. One of the advantages of the new method is the possibility of applying them to general systems without any constraints on the system matrices. In order to improve the performance and reduce conservatism of the SOF conditions, the Lyapunov matrix is considered parameter dependent. Numerical examples are presented to show the performance and effectiveness of the proposed methods.
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