The advantages of periodic control have been known since humanity learned to cultivate crops in rotation to increase production. In more recent times, it has been recognized that some industrial and technological systems also work or function better in a periodic fashion. Moreover, with periodic control laws it has been possible to solve problems for which no time-invariant solution exists. Periodic models are also able to describe the intrinsic periodicity in many natural phenomena and time series.

Periodic Systems gives a comprehensive treatment of the theory of time-varying dynamical systems with periodic coefficients, with special focus on the problems of filtering and control.

Topics covered include:

. basic issues like 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;

. 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 mathematics.

Zusammenfassung

Periodic Systems gives a comprehensive treatment of the theory of periodic systems, including the problems of filtering and control. Topics covered include: basic issues, including 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; 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 mathematics.

Inhalt
Linear Periodic Systems.- Floquet Theory and Stability.- Structural Properties.- Periodic Transfer Function and BIBO Stability.- Time-invariant Reformulations.- StateSpace Realization.- Zeros, Poles, and the Delay Structure.- Norms of Periodic Systems.- Factorization and Parametrization.- Stochastic Periodic Systems.- Filtering and Deconvolution.- Stabilization and Control.