Journal
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
Volume 24, Issue 16, Pages 2512-2521Publisher
WILEY
DOI: 10.1002/rnc.3006
Keywords
delay-dependent stability; discrete systems; linear matrix inequality; Lyapunov-Krasovskii functional; time-varying delays
Funding
- GRF HKU [7140/11E]
- National Natural Science Foundation of China [61074043, 61104117, 61174038]
- Specialized Research Fund for the Doctoral Program of Higher Education [20113219110026]
- 333 Project [BRA2011143]
- Qing Lan Project
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This paper proposes an improvement to the delay-dependent stability of discrete systems with time-varying delays. The approach is based on the observation that the positive definiteness of a chosen Lyapunov-Krasovskii functional does not necessarily require all the involved symmetric matrices to be positive definite, which has been overlooked in the literature. The derived delay-dependent stability conditions are in terms of linear matrix inequalities. It is theoretically proved that our results are less conservative than the corresponding ones obtained by requiring the positive definiteness of all the symmetric matrices in a chosen Lyapunov-Krasovskii functional. The importance of the present approach is that a great number of delay-dependent analysis and synthesis results obtained by the aforementioned requirement in the literature can be improved by the present approach without introducing any new decision variables. Copyright (c) 2013 John Wiley & Sons, Ltd.
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