Nonlinear system theory / John L. Casti.

Format:

Book

Author/Creator:

Casti, J. L.

Series:

Mathematics in science and engineering ; v. 175.

Mathematics in science and engineering ; v. 175

Language:

English

Subjects (All):

Nonlinear theories.

System analysis.

Physical Description:

1 online resource (275 p.)

Place of Publication:

Orlando : Academic Press, 1985.

Language Note:

English

Summary:

Nonlinear system theory

Contents:

Front Cover; Nonlinear System Theory; Copyright Page; Contents; Preface; Chapter 1. Perspectives and Problems of Nonlinear System Theory; I. A Nonlinear World; II. The Central Questions of System Theory; III. Classes of Nonlinear Processes; IV. Linear versus Nonlinear System Theory; Notes and References; Chapter 2. Mathematical Tools of Nonlinear System Theory; I. Introduction; II. Algebraic Concepts; III. Some Ideas from Differential Geometry; IV. Concepts from Algebraic Geometry; V. Grassmann Manifolds and the Classification Problem; Problems and Exercises; Notes and References

Chapter 3. A Modern View of Linear System TheoryI. Introduction; II. Mathematical Description of a Linear System; III. The Module Structure of θ, r, and ψ; IV. Some System-Theoretic Consequences; V. Transfer Functions; VI. Realization of Transfer Functions; VII. The Construction of Canonical Realizations; VIII. Partial Realizations; IX. Pole-Shifting and Stability; X. Some Geometric Aspects of Linear Systems; XI. Feedback, the McMillan Degree, and Kronecker Indices; Problems and Exercises; Notes and References; Chapter 4. Reachability and Controllability; I. Introduction

II. Basic Definitions and Problem StatementIll. Solution Manifolds for Dynamical Systems; IV. Some General Results; V. Linear-Analytic Systems; VI. The Role of the State Manifold M; VII. Bilinear Systems; VIII. Polynomial Systems; IX. Discrete-Time Systems; X. Input Construction; XI. Control Canonical Form and System Invariants; Problems and Exercises; Notes and References; Chapter 5. Observability, Realization, and Estimation; I. Measurements and State Determination; II. Some Basic Definitions; III. Basic Observability Results; IV. Polynomial Systems; V. Realization Theory

VI. Nonlinear Filtering and EstimationProblems and Exercises; Notes and References; Chapter 6. Stability Theory: Singularities, Bifurcations, and Catastrophes; I. Concepts of Stability; II. Lyapunov Stability; III. The Center Manifold Theorem; IV. Families of Vector Fields and Normal Forms; V. Elementary Bifurcations; VI. Singularity Theory and the Elementary Catastrophes; VII. Applications of Catastrophe Theory; VIII. Chaos and Strange Attractors; IX. Control Systems and Feedback; Problems and Exercises; Notes and References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28989-6

9786612289897

0-08-095865-6

OCLC:

316568496