The control and filtering of networked stochastic systems are an important part of modern control theory and engineering, and have extensive application background and scientific research value. However, complex phenomena such as measurement loss and channel attenuation caused by limited network bandwidth lead to the degradation of system performance, which brings huge challenges to the analysis and synthesis of random systems. Therefore, this project re-examines networked systems in the sense of randomness, combines mathematical tools such as probability theory and stochastic analysis with control theory, and proposes new ideas and methods for the research of control and filtering of stochastic systems. The research results obtained form a complete theoretical system for analyzing and processing the control and filtering problems of networked stochastic systems under communication constraints. With the support of several national-level projects such as the National Foundation of Nature and the New Century Outstanding Talent Program of the Ministry of Education, the main scientific findings are as follows: For random time-varying systems with communication constraints, the finite time domain Hinfin has been obtained for the first time; sufficient and necessary conditions for performance indicators. Based on this, a design framework for centralized, distributed controllers and filters in the form of backward recursive Riccati equations is established to improve the control and filtering of time-varying systems with communication constraints. Performance, obtained by IEEE Fellow, Professor Yuriy S. Good comments from Shmaliy. The concept of probability dependent gain mechanism and guaranteed probability set membership filtering theory are proposed, so that controllers and filters can be adjusted with changes in probability or modified with allowable probability requirements. For discrete random multi-agent systems, the consistency performance index in the sense of probability is redefined, and a sufficient condition for a class of discrete-time random systems to be stable based on probability input to state is proposed; Combined with an event-triggered protocol that reduces communication burden, a scalable distributed controller design technology that relies only on the eigenvalues of the network topology matrix is established. The results were obtained by IEEE Fellow, IFAC Fellow, InstMC Fellow, University of Texas Professor Frank L. The positive comments of Lewis and IEEE Fellow Professor Wei Kang at the University of Washington clearly pointed out that our method can effectively deal with network-induced complex phenomena while reducing communication burdens. For nonlinear time-varying random systems with limited communication, the impact of non-Gaussian noise and various network-induced phenomena on filtering accuracy is quantitatively analyzed, and new methods for designing envelopes constrained filters and error-limited filters in the mean-square sense are proposed. IEEE Fellow, IET Fellow, Professor James Lam of the University of Hong Kong, and Professor H. Vincent Poor evaluated the project to design a new type of filter that meets interval constraints from a mean-square perspective. For aperiodic sampled systems, the Vandermonde matrix is used to effectively deal with complex expectation operations induced by random sampling, the impact of aperiodic sampling interval on the stability performance of the entire sampled data system is quantitatively analyzed, and a controller design scheme to drive system stability is established. IEEE Fellow and Professor Qing-Long Han, Vice President of Swinburne University of Technology, affirmed the effectiveness of the project to quantitatively analyze the performance of aperiodic sampling systems from a discretization perspective. Eight representative papers in this project have been cited more than 600 times, five highly cited papers on ESI, and 7 published in the IEEE Journal of Automatic Control and Automatica, the top international journals in control disciplines. Project completers have won the New Century Outstanding Talent Plan of the Ministry of Education of China, the National Natural Fund of China and the Shanghai City Talent Plan.