Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 64, Issue 10, Pages 4209-4216Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2019.2893149
Keywords
Discretized Lyapunov functions; exponential stability; impulsive systems; L-2-gain; impulse delays
Funding
- National Natural Science Foundation of China [61573111, 61633011]
- Guangxi Natural Science Foundation [2018JJD170015]
- Australian Research Council [DP120104986]
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In this paper, the stability and L-2-gain properties of linear impulsive delay systems with delayed impulses are studied. Commonly employed techniques, in which the delayed impulses are treated using Newton-Leibniz formula. may not be applicable to L-2-gain analysis, since they make the disturbance input appear in the impulse part. In order to circumvent the difficulty, we first augment the considered system to a time-delay system with switching nondelayed impulses. Due to the absence of delayed impulses, this new approach has advantages in constructing Lyapunov functions and handling the effects of impulse delays on the system performance. Switching-based time-dependent Lyapunov functions are introduced to deal with the resultant switching impulses of the augmented system. Sufficient conditions for exponential stability and L-2-gain properties are derived in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach.
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