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Static output feedback stabilisation with ${H}_{\infty }$ performance for a class of plants. (English) Zbl 0974.93054
Summary: 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 nonlinear 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 ${H}_{\infty }$ performance objectives. This results in a sub-optimal static ${H}_{\infty }$ control law found by non-iterative means. The simplicity of the method is demonstrated by a numerical example.
##### MSC:
 93D15 Stabilization of systems by feedback 93B36 ${H}^{\infty }$-control 15A39 Linear inequalities of matrices 93B17 System transformation