Optimal control for systems with varying sampling rate

The paper addresses the aspects of control of real-time systems with varying sampling rate. To motivate, an example is given in which a stable continuous system is sampled at two different sampling rates. Two controllers are designed to minimize the same continuous quadratic loss function with the same weights. It is shown that although the design leads to stable controlled closed loop systems, for both discretizations, the resulting system can be unstable due to variations in sampling rate. To avoid that problem, we suggest an optimal controller design in which a bound on the cost, for all possible sampling rate variations, is computed. This results in a piecewise constant state feedback control law and guarantees stability regardless of the variations in sampling rate. The controller synthesis is cast into an LMI, which conveniently solves the synthesis problem. To illustrate the procedure, the introduction example is revise using the proposed LMI synthesis method and the stable control law is given, which is robustly stable against variations in sampling rate.