The second edition provides thorough, up-to-date coverage of the analytical foundations of various aspects of nonlinear systems. This includes details on existence and uniqueness of solutions and approximate analysis methods. Reflecting the increasing importance of digital computers, the author has included a discussion of discrete-time systems in the chapters dealing with Lyapunov stability and input-output stability. Several applications of nonlinear system theory are included throughout the book, including stability and convergence of adaptive identifiers, stability of a class of electro-mechanical systems, a separation theorem for deterministic nonlinear systems, and more.

Nonlinear Systems Analysis (Prentice-Hall Network Series / Prentice-Hall Electrical Engineering Series)

Science & Math

Vidyasagar, Mathukumalli

Mathematics

Prentice-Hall.Inc.

This brief introduces people with a basic background in probability theory to various problems in cancer biology that are amenable to analysis using methods of probability theory and statistics. The title mentions 'cancer biology' and the specific illustrative applications reference cancer data but the methods themselves are more broadly applicable to all aspects of computational biology. Aside from providing a self-contained introduction to basic biology and to cancer, the brief describes four specific problems in cancer biology that are amenable to the application of probability-based methods. The application of these methods is illustrated by applying each of them to actual data from the biology literature. After reading the brief, engineers and mathematicians should be able to collaborate fruitfully with their biologist colleagues on a wide variety of problems.

Computational Cancer Biology: An Interaction Network Approach (SpringerBriefs in Electrical and Computer Engineering)

Computers & Technology

Computer Science

Springer

This book introduces the so-called "stable factorization approach" to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be "factored" as a "ratio" of two matrices N,D whose elements belong to R, in such a way that N,D are coprime. In the familiar case where the ring R corresponds to the set of bounded-input, bounded-output (BIBO)-stable rational transfer functions, coprimeness is equivalent to two functions not having any common zeros in the closed right half-plane including infinity. However, the notion of coprimeness extends readily to discrete-time systems, distributed-parameter systems in both the continuous- as well as discrete-time domains, and to multi-dimensional systems. Thus the stable factorization approach enables one to capture all these situations within a common framework. 
 The key result in the stable factorization approach is the parametrization of all controllers that stabilize a given plant. It is shown that the set of all stabilizing controllers can be parametrized by a single parameter R, whose elements all belong to R. Moreover, every transfer matrix in the closed-loop system is an affine function of the design parameter R. Thus problems of reliable stabilization, disturbance rejection, robust stabilization etc. can all be formulated in terms of choosing an appropriate R. 
 This is a reprint of the book Control System Synthesis: A Factorization Approach originally published by M.I.T. Press in 1985. 
 Table of Contents: Introduction / Proper Stable Rational Functions / Scalar Systems: An Introduction / Matrix Rings / Stabilization

Control System Synthesis: A Factorization Approach (Synthesis Lectures on Control and Mechatronics, 2)

Engineering & Transportation

Engineering

Morgan Claypool

How does a machine learn a new concept on the basis of examples? This second edition takes account of important new developments in the field. It also deals extensively with the theory of learning control systems, now comparably mature to learning of neural networks.

Learning and Generalisation: With Applications to Neural Networks (Communications and Control Engineering)

Reference

Learning and Generalization: With Applications to Neural Networks

This book introduces the so-called ""stable factorization approach"" to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be ""factored"" as a ""ratio"" of two matrices N,D whose elements belong to R, in such a way that N,D are coprime. In the familiar case where the ring R corresponds to the set of bounded-input, bounded-output (BIBO)-stable rational transfer functions, coprimeness is equivalent to two functions not having any common zeros in the closed right half-plane including infinity. However, the notion of coprimeness extends readily to discrete-time systems, distributed-parameter systems in both the continuous- as well as discrete-time domains, and to multi-dimensional systems. Thus the stable factorization approach enables one to capture all these situations within a common framework.The key result in the stable factorization approach is the parametrization of all controllers that stabilize a given plant. It is shown that the set of all stabilizing controllers can be parametrized by a single parameter R, whose elements all belong to R. Moreover, every transfer matrix in the closed-loop system is an affine function of the design parameter R. Thus problems of reliable stabilization, disturbance rejection, robust stabilization etc. can all be formulated in terms of choosing an appropriate R.This is a reprint of the book Control System Synthesis: A Factorization Approach originally published by M.I.T. Press in 1985.Table of Contents: Introduction / Proper Stable Rational Functions / Scalar Systems: An Introduction / Matrix Rings / Stabilization

Control Systems Synthesis: A Factorization Approach, Part I (Synthesis Lectures on Control and Mechatronics)

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