caa a22 4500 445877871 CHVBK 20180317145533.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s11081-010-9120-4 doi (NATIONALLICENCE)springer-10.1007/s11081-010-9120-4 A nonlinear programming technique to compute atightlower bound for the real structured singular value [Elektronische Daten] [Ahmet Yazıcı, Abdurrahman Karamancıoğlu, Refail Kasimbeyli] The real structured singular value (RSSV, or real μ) is a useful measure to analyze the robustness of linear systems subject to structured real parametric uncertainty, and surely a valuable design tool for the control systems engineers. We formulate the RSSV problem as a nonlinear programming problem and use a new computation technique, F-modified subgradient (F-MSG) algorithm, for its lower bound computation. The F-MSG algorithm can handle a large class of nonconvex optimization problems and requires no differentiability. The RSSV computation is a well known NP hard problem. There are several approaches that propose lower and upper bounds for the RSSV. However, with the existing approaches, the gap between the lower and upper bounds is large for many problems so that the benefit arising from usage of RSSV is reduced significantly. Although the F-MSG algorithm aims to solve the nonconvex programming problems exactly, its performance depends on the quality of the standard solvers used for solving subproblems arising at each iteration of the algorithm. In the case it does not find the optimal solution of the problem, due to its high performance, it practically produces a very tight lower bound. Considering that the RSSV problem can be discontinuous, it is found to provide a good fit to the problem. We also provide examples for demonstrating the validity of our approach. Springer Science+Business Media, LLC, 2010 Robust control nationallicence Real structured singular value nationallicence Nonlinear programming nationallicence Modified subgradient algorithm nationallicence Yazıcı Ahmet Computer Engineering Department, Osmangazi University, 26480, Eskişehir, Turkey aut Karamancıoğlu Abdurrahman Electrical Engineering Department, Osmangazi University, 26480, Eskişehir, Turkey aut Kasimbeyli Refail Department of Industrial Systems Engineering, Izmir University of Economics, 35330, Izmir, Turkey aut Optimization and Engineering Springer US; http://www.springer-ny.com 12/3(2011-09-01), 445-458 1389-4420 12:3<445 2011 12 11081 https://doi.org/10.1007/s11081-010-9120-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11081-010-9120-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yazıcı Ahmet Computer Engineering Department, Osmangazi University, 26480, Eskişehir, Turkey aut NATIONALLICENCE 700 1- Karamancıoğlu Abdurrahman Electrical Engineering Department, Osmangazi University, 26480, Eskişehir, Turkey aut NATIONALLICENCE 700 1- Kasimbeyli Refail Department of Industrial Systems Engineering, Izmir University of Economics, 35330, Izmir, Turkey aut NATIONALLICENCE 773 0- Optimization and Engineering Springer US; http://www.springer-ny.com 12/3(2011-09-01), 445-458 1389-4420 12:3<445 2011 12 11081 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer