How the brain's white-matter anatomy constrains brain activity is an open question that might give insights into the mechanisms that underlie mental disorders such as schizophrenia. Chromosome 22q11.2 deletion syndrome (22q11DS) is a neurodevelopmental disorder with an extremely high risk for psychosis providing a test case to study developmental aspects of schizophrenia. In this study, we used principles from network control theory to probe the implications of aberrant structural connectivity for the brain's functional dynamics in 22q11DS. We retrieved brain states from resting-state functional magnetic resonance images of 78 patients with 22q11DS and 85 healthy controls. Then, we compared them in terms of persistence control energy; that is, the control energy that would be required to persist in each of these states based on individual structural connectivity and a dynamic model. Persistence control energy was altered in a broad pattern of brain states including both energetically more demanding and less demanding brain states in 22q11DS. Further, we found a negative relationship between persistence control energy and resting-state activation time, which suggests that the brain reduces energy by spending less time in energetically demanding brain states. In patients with 22q11DS, this behavior was less pronounced, suggesting a deficiency in the ability to reduce energy through brain activation. In summary, our results provide initial insights into the functional implications of altered structural connectivity in 22q11DS, which might improve our understanding of the mechanisms underlying the disease.