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New relaxed stabilization conditions for discrete‐time Takagi–Sugeno fuzzy control systems
Author(s) -
Kong Lei,
Yuan Jingqi
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2047
Subject(s) - control theory (sociology) , compensation (psychology) , conservatism , fuzzy control system , lyapunov function , fuzzy logic , convexity , control (management) , mathematics , function (biology) , mathematical optimization , discrete time and continuous time , matrix (chemical analysis) , computer science , nonlinear system , law , artificial intelligence , economics , materials science , psychoanalysis , financial economics , composite material , biology , psychology , quantum mechanics , evolutionary biology , political science , physics , politics , statistics
This paper develops relaxed stabilization conditions for discrete‐time Takagi–Sugeno fuzzy control systems based on the extended nonquadratic Lyapunov function, the nonparallel distributed compensation law, and the convexity of the fuzzy blending coefficients. Three new main results are proposed to further reduce the conservatism by fully exploring the slack matrix technique and introducing new slack matrices and extra collection matrices. The new stabilization conditions are gradually less and less conservative, and more advantageous than the existing results by overall consideration of the conservatism and the computational efforts. A well‐known numerical case and a practical case are carried out to demonstrate the effectiveness of the proposed stabilization conditions.