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.

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, including the problems of filtering and control.

Topics covered include:

a [ basic issues, including Floquet theory, controllability and observability, canonical decomposition, system norms and Lyapunov and robust stability;

a [ the problem of state estimation in its various forms, filtering, prediction and smoothing;

a [ 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 authorsa (TM) 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.

Control systems design methodologies have long suffered the traditional and myopic dichotomy between time and frequency domain approaches, each of them being specialized to cope with only scarcely overlapping performance requirements. This book is aimed at bridging the two approaches by presenting design methodologies based on the minimization of a norm (H2/H() of a suitable transfer function. A distinctive feature of these techniques is the fact that they do not create only one solution to the design problem, instead they provide a whole set of admissible solutions which satisfy a constraint on the maximum deterioration of the performance index.
A systematic book on this topic is long overdue. Self-contained and practical in its approach, Control Theory and Design enables the reader to use the relevant techniques in various real-life applications. The text covers the basic facts of robustcontrol and theory as well as more recent achievements, such as robust stability and robust performance in presence of parameter uncertainties. It features a new perspective on classical LQC results and further sections on robust synthesis, nonclassicaloptimization problems, and analysis and synthesis of uncertain systems.
Control Theory and Design is essential reading for graduates and those entering the research field. The required mathematical background is provided so that the book is also suitable for undergraduate students with some knowledge of basic systemsand control.
Key Features
* Provides a self-contained manual for learning control systems and design
* Contains a clear and concise presentation of the technical background needed
* Includes a new perspective of classical LQG results
* Contains updated results and novel contributions to nonstandard RH2/RH infinity symbol problems
* Covers all the theory from the basic to the more advanced issues

Positive Markov Jump Linear Systems are piecewise positive linear systems affected by a stochastic signal generated by a Markov chain. Positive systems naturally arise in the description of biological systems, compartmental models, population dynamics, traffic modeling, chemical reactions, queue processes, and so on. A rich literature on positive linear systems is now available. This is the first work to provide an overview of these developments. It outlines the typical applications of such systems, giving a detailed description of the mathematical theory underpinning the subject. It provides a comprehensive and timely introduction to the study of such systems. Readers who are new to the topic will find everything required to understand such systems in a concise and accessible form.

Positive systems are an important class of systems that frequently arise in application areas, such as in the chemical process industry, electronic circuit design, communication networks, and biology. The study of the stability of such systems differs from standard systems in that the analysis focuses only on the trajectories generated under positivity constraints. Switched positive systems also arise in a variety of applications. Examples can be found in TCP congestion control, in processes described by non-homogeneous Markov chains, in image processing, in biochemical networks, and so on. In comparison to general switched systems, that have received a lot of attention in the past years, the theory for positive switched systems is still in its infancy. Switched Positive Linear Systems studies the stability, performance evaluation, stabilization via switching control, and optimal control of (continuous-time and linear) positive switched systems. It provides a review of the results that have already been established in the literature. Other results, especially those related to norm computation and optimization, are new and are presented integrated with previous ones. This book provides a comprehensive and timely introduction to the study of such systems. Readers who are new to the topic will find everything required to understand such systems in a concise and accessible form.