Reflection-based technique for synthesis of structured controllers with guaranteed local convergence

Mohamed Yagoubi and Redouane Chaibi

International Journal of Systems Science, 2020, vol. 51, issue 16, 3491-3502

Abstract: This paper deals with stabilisation, $H_2 $H2 and $H_\infty $H∞ static output feedback synthesis, under structure constraints for linear time-invariant systems. The proposed approach relies on a prominent property of Hurwitz-stable matrices set and a Douglas-Rachford (DR) reflection method type for finding a point in the intersection of two closed sets. The method proposed in this paper emulates the genericity of the Linear Matrix Inequalities framework while keeping the feedback gain separated from any matrix with direct or indirect connection to the Lyapunov function. The link between the sequence of iterates generated by the proposed algorithm and a continuous dynamical system results in the use of Lyapunov stability theory for guaranteeing the local convergence. Several examples are given to prove the validity of the proposed method.

Date: 2020
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DOI: 10.1080/00207721.2020.1817612

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