Abstract
Abstract This paper studies the controllability of complex-valued impulsive systems with time-varying delays in control input. The impulsive systems considered here have a complex-valued state space, for some typical examples such as biological neural networks and quantum systems can be described by such systems. Using the method of variation of parameters, an explicit expression of the solution for the given system is established. Based on the solution so obtained, several controllability criteria are presented for such systems. Necessary and sufficient conditions for controllability are further derived for the time-invariant case. It is shown that controllability of such systems is dependent on the impulsive function in discrete time, the system matrices in continuous time, and the time delay in control. Three numerical examples are presented to demonstrate the effectiveness of the developed controllability results.
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