Stochastic Analysis and Synthesis of Networked Systems With Consecutively Lost Packets
研究了采样数据下连续丢包网络化系统的H∞控制问题，建立了离散随机系统模型，通过矩阵指数计算和期望求解设计控制器，保证指数均方稳定性和H∞性能，且线性矩阵不等式维数不随最大连续丢包数增加。
This study is concerned with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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.