The optimal sampling pattern for linear control systems

In digital control systems the state is sampled at given sampling instants and the input is kept constant between two consecutive instants. By optimal sampling problem we mean the selection of sampling instants and control inputs, such that a given function of the state and input is minimized. In this paper we formulate the optimal sampling problem and we propose a numerical method to solve it. Being the solving procedure time consuming, we also propose a new quantization-based sampling strategy that is computationally tractable and capable to achieve a near-optimal cost. Finally, we prove that the quantization-based sampling is optimal in scalar systems for large number of samples.