Metadata only entryThis paper was published as Systems and Control Letters, 2001, 43 (3), pp.159-166. It is available from http://www.sciencedirect.com/science/journal/01676911. Doi: 10.1016/S0167-6911(01)00087-1In this paper, the problem of static output feedback control of a linear system is considered. The existence of a static output feedback control law is given in terms of the solvability of two coupled Lyapunov inequalities which result in a non-linear optimisation problem. However, using state-coordinate and congruence transformations and by imposing a block-diagonal structure on the Lyapunov matrix, we will see that the determination of a static output feedback gain reduces, for a specific class of plants, to finding the solution of a system of linear matrix inequalities. The class of plants considered is those which are minimum phase with a full row rank Markov parameter. The method is extended to incorporate H∞ performance objectives. This results in a sub-optimal static H∞ control law found by non-iterative means. The simplicity of the method is demonstrated by a numerical example
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