Linear Stochastic Systems : A Geometric Approach to Modeling, Estimation and Identification / by Anders Lindquist, Giorgio Picci.

Format:

Book

Author/Creator:

Lindquist, Anders, Author.

Picci, Giorgio., Author.

Series:

Contemporary mathematics, 2364-009X 0271-4132 1

Contemporary mathematics, 2364-009X ; 0271-4132 1

Language:

English

Subjects (All):

System theory.

Probabilities.

Automatic control.

Systems Theory, Control.

Probability Theory and Stochastic Processes.

Control and Systems Theory.

Local Subjects:

Systems Theory, Control.

Probability Theory and Stochastic Processes.

Control and Systems Theory.

Physical Description:

1 online resource (788 p.)

Edition:

1st ed. 2015.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.

Language Note:

English

Summary:

This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notion of the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory.

Contents:

Introduction

Geometry of Second-Order Random Processes

Spectral Representation of Stationary Processes

Innovations, Wold Decomposition, and Spectral Factorization

Wold Decomposition and Spectral Factorization in Continuous Time

Linear Finite-Dimensional Stochastic Systems

The Geometry of Splitting Subspaces

Markovian Representations

Proper Markovian Representations in Hardy Space

Stochastic Realization Theory in Continuous Time

Stochastic Balancing and Model Reduction

Finite-Interval Stochastic Realization and Partial Realization Theory

Subspace Identification for Time Series

Zero Dynamics and the Geometry of the Riccati Inequality

Smoothing and Interpolation

Acausal Linear Stochastic Models and Spectral Factorization

Stochastic Systems with Inputs

Appendix A. Basic Principles of Deterministic Realization Theory

Appendix B. Some Topics in Linear Algebra and Hilbert Space Theory.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

3-662-45750-4