Abstract:
The circle criterion (for continuous-time systems) and Tsypkin's criterion (for discrete-time systems) of absolute stability for Lurie systems with several nonlinearities are obtained with the use of the convolution theorem and without use of the $S$-procedure. On the basis of the convolution theorem, two theorems are proved which lead to a substantial reduction in the dimension of connected systems of linear matrix inequalities.
Bibliography: 19 titles.
Keywords:absolute stability of Lurie systems, matrix inequalities, circle criterion, Tsypkin's criterion, $S$-procedure.
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