In this paper, we study digital control systems with non-uniform updating and sampling patterns, which include multirate sampled-data systems as special cases. First, we derive lifted models in the state-space domain, and give a sufficient condition under which the lifted models preserve controllability and observability. The main obstacle for generalized predictive control (GPC) design using the lifted models is the so-called causality constraint. Taking into account this design constraint, we propose a new GPC algorithm, which results in optimal causal control laws for the non-uniformly sampled systems and applies immediately to multirate sampled-data systems.