Control of sampled data systems with variable sampling rate

This paper addresses stability and performance of sampled-data systems with variable sampling rate, where the change between sam- pling rates is decided by a scheduler. A motivational example is pre- sented, where a stable continuous time system is controlled with two sampling rates. It is shown that the resulting system could be unsta- ble when the sampling changes between these two rates, although each individual closed-loop system is stable under the designed controller that minimizes the same continuous loss function. Two solutions are presented in this paper. The ¯rst solution is to impose restrictions on switching sequences such that only stable sequences are chosen. The second solution presented is more general, where a piecewise constant state feedback control law is designed which guarantees stability for all possible variations of sampling rate. Furthermore, the performance definedn by a continuous time quadratic cost function for the sampled-data system with variable sampling rate can be optimised using the proposed synthesis method.