In this chapter, issues of fault detection and estimation for linear discrete time-varying (LDTV) systems are addressed by using Krein space projection technique in the framework of \(H_\infty \) filtering. Firstly, an \(H_\infty \) fault detection filter (FDF) is constructed for residual generation, the design of which is formulated as a minimization problem of a certain quadratic form. Then, by means of projection and innovation analysis in Krein spaces, a solution to such an \(H_\infty \) -FDF is derived. Moreover, to estimate faults in LDTV systems with a reduced communication rate, an event-triggered \(H_\infty \) filter is constructed. By equivalently converting the \(H_\infty \) filtering issue into a certain minimization problem of indefinite quadratic form subject to LDTV systems with non-uniform sampling periods, a Krein space projection-based solution to the event-triggered \(H_\infty \) fault estimator is derived in terms of Riccati recursions, achieving a complete decoupling of estimation error from the event-triggered transmission error. Also, a less conservative and more computationally attractive implementation algorithm is developed.