Stochastic Analysis and Synthesis of Networked Systems With Consecutively Lost Packets

This study is concerned with the H-infinity control issue of networked systems with consecutively lost packets using sampled-data. First, we establish a discrete stochastic system for the networked system with external disturbances and consecutively lost packets. To enable H-infinity performance analysis, an equivalent but analyzable stochastic framework is then derived by using matrix exponential computation. Subsequently, by law of total expectation, Kronecker product operation, and eigenvalue decomposition approach, we compute the expectation of a coupling term with significant nonlinearity and randomness. Based on this, a stabilization controller is constructed that ensures the resulting discrete stochastic system's exponential mean-square stability with a prescribed H-infinity performance. Unlike the existing literature, the linear matrix inequalitys (LMIs) dimension derived in this article does not change along with the maximum number of consecutively lost packets, which prevents an LMI with high-computing complexity. Finally, the validity and applicability of the algorithm are demonstrated by a numerical example and an example using a satellite system.