Periodic Systems gives a comprehensive treatment of the theory of periodic systems, including the problems of filtering and control. Topics covered include basic issues, such as Floquet theory, controllability and observability, canonical decomposition, system norms, and Lyapunov and robust stability; the problem of state estimation in its various forms, filtering, prediction, and smoothing; and control design methods, particularly optimal and robust control. The text focuses on discrete-time signals and systems; however, an overview of the entire field, including the continuous-time case, is provided in the first chapter. The authors' presentation of the theory and results is mathematically rigorous while maintaining a readable style, avoiding excessive formalism. This makes the book accessible to graduate students and researchers from the fields of engineering, physics, economics, and math.