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Danik Y E. LMI-based robustness analysis of the nonlinear regulator for discrete time nonlinear systems. ITCMS. 2017; 3 (1) :1-8
URL: http://europeansp.org/article-11-184-en.html
Abstract:   (67 Views)
In this paper the new approach of nonlinear control synthesis based on the discrete state dependent Riccati equation (D-SDRE) obtained from the application of the discrete maximum principle is proposed. It deals with formally weakly nonlinear systems and allows to get a numerical-analytical algorithm for stabilizing regulator construction. The robustness analysis of a proposed stabilizing controller for quasi-linear state dependent coefficients discrete systems is investigated under interval static parametric uncertainties in the linear part of the initial system. The presence of only formally weak nonlinearity allows to study the robustness of the system based on the robustness of the corresponding unperturbed discrete linear system using linear matrix inequalities (LMI) approach. The proposed nonlinear stabilizing regulator is calculated at the average values of the uncertainty parameters and is used for all realizations of the uncertainties in the system. The corresponding robustness theorem is formulated. A number of numerical experiments on the discrete model of an inverted pendulum are performed. This work was supported by the Russian Science Foundation (Project No. 16-11-00048). © 2016 The Authors. Published by European Science publishing Ltd. Selection and peer-review under responsibility of the Organizing Committee of European Science publishing Ltd.
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Received: 2019/08/8 | Accepted: 2019/08/8 | Published: 2019/08/8

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