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L 1 synthesis of a static output controller for positive systems by LMI iteration
Author(s) -
Saeki Masami
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3956
Subject(s) - mathematics , linear matrix inequality , output feedback , control theory (sociology) , sequence (biology) , regular polygon , convex optimization , matrix (chemical analysis) , positive definite matrix , convex combination , monotonic function , lyapunov function , controller (irrigation) , mathematical optimization , nonlinear system , computer science , control (management) , mathematical analysis , eigenvalues and eigenvectors , materials science , geometry , physics , quantum mechanics , artificial intelligence , biology , agronomy , composite material , genetics
Summary An approach to find a static output feedback gain that makes the feedback system positive and minimizes the L 1 gain is proposed. The problem of finding a static output feedback gain has 3 aspects: stabilizing the system, making the system positive, and then minimizing the L 1 gain. Each subproblem is described by bilinear matrix inequality with respect to the feedback gain and the Lyapunov matrix or vector. Linear matrix inequality (LMI) that is sufficient to satisfy bilinear matrix inequality is derived using a convex‐concave decomposition, and the feedback gain sequence is calculated by an iterative solution of LMI. The sequence of the upper bounds on the design parameter is guaranteed to be monotonically nonincreasing for each algorithm. Similarly, 2 other LMIs are derived for each subproblem using another convex‐concave decomposition and PK iteration. The effectiveness of these algorithms is illustrated via several numerical examples.