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Event‐triggered constrained control of positive systems with input saturation
Author(s) -
Yin Yanyan,
Lin Zongli,
Liu Yanqing,
Teo Kok Lay
Publication year - 2018
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.4097
Subject(s) - orthant , mathematics , convex hull , control theory (sociology) , linear matrix inequality , domain (mathematical analysis) , linear system , convex optimization , optimization problem , state (computer science) , lyapunov function , mathematical optimization , matrix (chemical analysis) , regular polygon , computer science , control (management) , nonlinear system , algorithm , mathematical analysis , geometry , materials science , artificial intelligence , composite material , physics , quantum mechanics
Summary This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.