Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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Monografia | Biblioteca da UMinho no Campus de Azurém | BPG3 517.9 - V | Available | 322650 |

Total holds: 0

When M. Vidyasagar wrote the first edition of this book, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature.

The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. In addition, it includes valuable reference material in these chapters that is unavailable elsewhere. The text also features a large number of problems that allow readers to test their understanding of the subject matter and self-contained sections and chapters that allow readers to focus easily on a particular topic.

**Preface to the Classics Edition**(p. xiii)**Preface**(p. xv)**Note to the Reader**(p. xvii)**1. Introduction**(p. 1)**2. Nonlinear Differential Equations**(p. 6)**2.1 Mathematical Preliminaries**(p. 6)**2.2 Induced Norms and Matrix Measures**(p. 19)**2.3 Contraction Mapping Theorem**(p. 27)**2.4 Nonlinear Differential Equations**(p. 33)**2.5 Solution Estimates**(p. 46)**3. Second-Order Systems**(p. 53)**3.1 Preliminaries**(p. 53)**3.2 Linearization Method**(p. 57)**3.3 Periodic Solutions**(p. 67)**3.4 Two Analytical Approximation Methods**(p. 79)**4. Approximate Analysis Methods**(p. 88)**4.1 Describing Functions**(p. 88)**4.2 Periodic Solutions: Rigorous Arguments**(p. 109)**4.3 Singular Perturbations**(p. 127)**5. Lyapunov Stability**(p. 135)**5.1 Stability Definitions**(p. 135)**5.2 Some Preliminaries**(p. 147)**5.3 Lyapunov's Direct Method**(p. 157)**5.4 Stability of Linear Systems**(p. 193)**5.5 Lyapunov's Linearization Method**(p. 209)**5.6 The Lur'e Problem**(p. 219)**5.7 Converse Theorems**(p. 235)**5.8 Applications of Converse Theorems**(p. 246)**5.9 Discrete-Time Systems**(p. 264)**6. Input-Output Stability**(p. 270)**6.1 L[subscript p]-Spaces and their Extensions**(p. 271)**6.2 Definitions of Input-Output Stability**(p. 277)**6.3 Relationships Between I/O and Lyapunov Stability**(p. 284)**6.4 Open-Loop Stability of Linear Systems**(p. 292)**6.5 Linear Time-Invariant Feedback Systems**(p. 309)**6.6 Time-Varying and/or Nonlinear Systems**(p. 337)**6.7 Discrete-Time Systems**(p. 365)**7. Differential Geometric Methods**(p. 376)**7.1 Basics of Differential Geometry**(p. 377)**7.2 Distributions, Frobenius Theorem**(p. 392)**7.3 Reachability and Observability**(p. 399)**7.4 Feedback Linearization: Single-Input Case**(p. 427)**7.5 Feedback Linearization: Multi-Input Case**(p. 438)**7.6 Input-Output Linearization**(p. 456)**7.7 Stabilization of Linearizable Systems**(p. 464)**A. Prevalence of Differential Equations with Unique Solutions**(p. 469)**B. Proof of the Kalman-Yacubovitch Lemma**(p. 474)**C. Proof of the Frobenius Theorem**(p. 476)**References**(p. 486)**Index**(p. 493)

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