This paper investigates controllability for linear time-invariant systems under irregular and random sampling, and develops adaptive control algorithms with respect to sampling intervals. Using block erasure channels as the main motivating communication platform, it first establishes a sufficient condition on sampling density that ensures controllability of sampled systems, which is necessary for feedback design and adaptation. Then, it continues with causal adaptive feedback algorithms to accommodate time-varying sampling intervals. Implementation of such algorithms encounters technical challenges because future sampling intervals are uncertain or random. Under deterministic slowly-varying and stochastic infrequent Markovian jumping sampling intervals, overall system stability is established. Simulation results are used to illustrate the algorithms and their effectiveness. (C) 2015 Elsevier Ltd. All rights reserved.