LQG control for sampled-data systems under stochastic sampling

This paper studies the linear-quadratic-Gaussian (LQG) problem for sampled-data systems with a stochastic sampling interval obeying a certain probability distribution. An optimal estimator of the system state is presented by the standard Kalman filter, and the Vandermonde matrix and Kronecker product operation are used to calculate the mathematical expectation caused by stochastic sampling in the process of designing the LQG controller. Moreover, it was proved that the controller can ensure the system is exponentially mean square stable. Finally, some simulation results are given to verify the effectiveness and practicability of the proposed controller design method.