Transient patterns of interregional connectivity form and dissipate in response to varying cognitive demands. Yet, it is not clear how different cognitive demands influence brain state dynamics, and whether these dynamics relate to general cognitive ability. Here, using functional magnetic resonance imaging (fMRI) data, we characterised shared, recurrent, global brain states in 187 participants across the working memory, emotion, language, and relation tasks from the Human Connectome Project. Brain states were determined using Leading Eigenvector Dynamics Analysis (LEiDA). In addition to the LEiDA-based metrics of brain state lifetimes and probabilities, we also computed information-theoretic measures of Block Decomposition Method of complexity, Lempel-Ziv complexity and transition entropy. Information theoretic metrics are notable in their ability to compute relationships amongst sequences of states over time, compared to lifetime and probability, which capture the behaviour of each state in isolation. We then related task-based brain state metrics to fluid intelligence. We observed that brain states exhibited stable topology across a range of numbers of clusters (K = 2:15). Most metrics of brain state dynamics, including state lifetime, probability, and all information theoretic metrics, reliably differed between tasks. However, relationships between state dynamic metrics and cognitive abilities varied according to the task, the metric, and the value of K, indicating that there are contextual relationships between task-dependant state dynamics and trait cognitive ability. This study provides evidence that the brain reconfigures across time in response to cognitive demands, and that there are contextual, rather than generalisable, relationships amongst task, state dynamics, and cognitive ability.