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Zbl 1133.93362
Yang, Zhichun; Xu, Daoyi
Robust stability of uncertain impulsive control systems with time-varying delay. (English)
[J] Comput. Math. Appl. 53, No. 5, 760-769 (2007). ISSN 0898-1221

Summary: We are concerned with the robust stability problem of an uncertain impulsive control system with time-varying delay. By employing the formula for the variation of parameters and estimating the Cauchy matrix, several criteria on robust exponential stability are derived and the exponential convergence rate is estimated. Based on $P$-norm and $P$-measure of matrix, it is seen that our sufficient conditions are less restrictive than the ones in the earlier publication. Some numerical examples and simulations are given to illustrate the theoretical results and to show that the criteria can be applied to stabilize the unstable continuous system with time delays and uncertainties by utilizing impulsive control.

MSC 2000:: *93D09 Robust stability of control systems
93C41 Control problems with incomplete information
93B35 Sensitivity (robustness) of control systems

Keywords: impulsive control; time delay; uncertainty; exponential stability; robustness

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