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Event‐triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach
Author(s) -
Yin Yanyan,
Liu Yanqing,
Teo Kok Lay,
Wang Song
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.3858
Subject(s) - probabilistic logic , mathematical optimization , linear matrix inequality , convex optimization , optimization problem , norm (philosophy) , bounded function , control theory (sociology) , convex hull , computer science , linear system , domain (mathematical analysis) , mathematics , regular polygon , control (management) , law , mathematical analysis , geometry , artificial intelligence , political science
Summary This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example.