Periodic Systems: Filtering And Control (communications And Control Engineering)

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. 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. Front Matter....Pages i-xix Introduction....Pages 1-59 Linear Periodic Systems....Pages 61-80 Floquet Theory and Stability....Pages 81-108 Structural Properties....Pages 109-154 Periodic Transfer Function and BIBO Stability....Pages 155-170 Time-invariant Reformulations....Pages 171-192 State–Space Realization....Pages 193-213 Zeros, Poles, and the Delay Structure....Pages 215-234 Norms of Periodic Systems....Pages 235-264 Factorization and Parametrization....Pages 265-289 Stochastic Periodic Systems....Pages 291-310 Filtering and Deconvolution....Pages 311-352 Stabilization and Control....Pages 353-405 Back Matter....Pages 407-424