State feedback controller design of networked sampled-data systems with packet loss

In this paper, the stabilization problem of linear networked sampled-data systems subject to packet loss is studied. First, by discrete-time approach, we establish a discrete-time unified framework. Then, an equivalent stochastic model is constructed in virtue of matrix exponential computation, where the system matrix is characterized by high nonlinearity and randomness with respect to the number of consecutive packet dropouts, which poses difficulties for the expectation operation of a nonlinear and random coupling term in the analysis of the resulting stochastic system. In order to deal with the difficulties, the law of total expectation, confluent Vandermonde matrix and Kronecker product operation are used and then a stabilization controller is designed such that the stochastic stability of the closed-loop stochastic system is guaranteed. Finally, a numerical example and an example using inverted pendulum system are given to show the effectiveness and applicability of the designed algorithm.