Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.

This book collects the lectures given at the NATO Advanced Study Institute From Identijication to Learning held in Villa Olmo, Como, Italy, from August 22 to September 2, 1994. The school was devoted to the themes of Identijication, Adaptation and Learning, as they are currently understood in the Information and Contral engineering community, their development in the last few decades, their inter connections and their applications. These titles describe challenging, exciting and rapidly growing research areas which are of interest both to contral and communication engineers and to statisticians and computer scientists. In accordance with the general goals of the Institute, and notwithstanding the rat her advanced level of the topics discussed, the presentations have been generally kept at a fairly tutorial level. For this reason this book should be valuable to a variety of rearchers and to graduate students interested in the general area of Control, Signals and Information Pracessing. As the goal of the school was to explore a common methodologicalline of reading the issues, the flavor is quite interdisciplinary. We regard this as an original and valuable feature of this book."

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.

Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.

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.

This book collects the lectures given at the NATO Advanced Study Institute From Identijication to Learning held in Villa Olmo, Como, Italy, from August 22 to September 2, 1994. The school was devoted to the themes of Identijication, Adaptation and Learning, as they are currently understood in the Information and Contral engineering community, their development in the last few decades, their inter connections and their applications. These titles describe challenging, exciting and rapidly growing research areas which are of interest both to contral and communication engineers and to statisticians and computer scientists. In accordance with the general goals of the Institute, and notwithstanding the rat her advanced level of the topics discussed, the presentations have been generally kept at a fairly tutorial level. For this reason this book should be valuable to a variety of rearchers and to graduate students interested in the general area of Control, Signals and Information Pracessing. As the goal of the school was to explore a common methodologicalline of reading the issues, the flavor is quite interdisciplinary. We regard this as an original and valuable feature of this book."

This volume contains five tutorial papers based on the lectures given at the intensive course on Software Reliability Modelling and Identification in Como (Italy) from September 2 to 4, 1987. The purpose of this volume is to present some important models used to forecast the reliability growth during the software testing process, and discuss the practical applicability of models in the management of software techniques for model identification from data (parameter estimation, complexity selection, validation, etc.). The basic reliability concepts are also introduced for those readers who are not familiar with the reliability ideas. Besides the basic models, a new family of models is introduced in the book. This family is flexible enough to describe a variety of different reliability trends. Particular attention is given to the problem of the provision of tools to assist the user in selecting an appropriate model in a particular situation.