Abstract
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
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Foundation item: Project (60425310) supported by the National Natural Science Foundation of China; project (2001AA4422200) supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China
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Liu, Xg., Wu, M. Robust stability of discrete-time nonlinear system with time-delay. J Cent. South Univ. Technol. 12 (Suppl 1), 227–231 (2005). https://doi.org/10.1007/s11771-005-0404-3
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DOI: https://doi.org/10.1007/s11771-005-0404-3