Controllability and adaptation of linear time-invariant systems under irregular and Markovian sampling

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.