During the past two decades, theVariance-constrained filtering variance-constrained filteringVariance-constrained filtering and estimation issues have been one of the dominant research topics on account of their great application potentials in a variety of research areas, such as imagine processing, target tracking and environmental monitoring. Along with the rapid advancements of network communication techniques, compared with the traditional control systems, the networked control systemsNetworked control system possess prominent merits including flexible architecture, decreased maintenance cost, high reliability and so on. While the network communication brings some convenience, a series of network-induced phenomenaNetwork-induced phenomena generally emerge in the process of signal transmissionSignal transmission due to constrainedNetwork bandwidth network bandwidthConstrained network bandwidth, unreliable communicationUnreliable communication link and complicated network environment, such as missing measurement, fading measurementFading measurement, sensor saturationSensor saturation, sensor delaySensor delay, network attacksNetwork attack, and so on. In addition, it is worth emphasizing that because of the modeling errorModeling error or implementation error, some imperfect internal features regarding the dynamical systems might appear including stochastic uncertainty, stochastic nonlinearityNonlinearity and so on. On the other hand, it is noted that the systems are always time-varying in practical engineering applications on account of the complicated network media. As a result, it is crucial to tackle the filtering and estimation issues for time-varying dynamical systemsTime-varying dynamical system affected by the incomplete informationIncomplete information (networked-induced phenomena, modeling uncertainty and so on) under variance-constrained senseVariance-constrained sense, which serves as a meaningful yet challenging topic.