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Zbl 0974.93054
Prempain, E.; Postlethwaite, I.
Static output feedback stabilisation with $H_{\infty}$ performance for a class of plants. (English)
[J] Syst. Control Lett. 43, No.3, 159-166 (2001). ISSN 0167-6911

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 2000:: *93D15 Stabilization of systems by feedback
93B36 $H^\infty$-control
15A39 Linear inequalities
93B17 System transformation

Keywords: output feedback; linear systems; linear matrix inequalities; coupled Lyapunov inequalities; transformations; block-diagonal structure; Lyapunov matrix; $H_\infty$ control

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Zentralblatt MATH Berlin [Germany]