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Induced L 2 ‐norm control for LPV systems with bounded parameter variation rates
Author(s) -
Wu Fen,
Yang Xin Hua,
Packard Andy,
Becker Greg
Publication year - 1996
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/(sici)1099-1239(199611)6:9/10<983::aid-rnc263>3.0.co;2-c
Subject(s) - bounded function , control theory (sociology) , mathematics , bounding overwatch , norm (philosophy) , lyapunov function , parameter space , convex optimization , attenuation , controller (irrigation) , regular polygon , finite set , bounded variation , mathematical optimization , control (management) , computer science , mathematical analysis , nonlinear system , physics , artificial intelligence , political science , law , agronomy , statistics , geometry , optics , quantum mechanics , biology
A linear, finite‐dimensional plant, with state‐space parameter dependence, is controlled using a parameter‐dependent controller. The parameters whose values are in a compact set, are known in real time. Their rates of variation are bounded and known in real time also. The goal of control is to stabilize the parameter‐dependent closed‐loop system, and provide disturbance/error attenuation as measured in induced L 2 norm. Our approach uses a bounding technique based on a parameter‐dependent Lyapunov function, and then solves the control synthesis problem by reformulating the existence conditions into a semi‐infinite dimensional convex optimization. We propose finite dimensional approximations to get sufficient conditions for successful controller design.