# Continuous-Time Systems

• Yuriy Shmaliy
• Electronic systems

• Linear time-invariant systems

• Linear time-varying systems

• Nonlinear time-invariant systems

• Nonlinear time-varying systems

Book

1. Front Matter
Pages I-XVII
2. Yuriy Shmaliy
Pages 1-42
3. Yuriy Shmaliy
Pages 43-118
4. Yuriy Shmaliy
Pages 119-152
5. Yuriy Shmaliy
Pages 153-237
6. Yuriy Shmaliy
Pages 239-347
7. Yuriy Shmaliy
Pages 349-423
8. Yuriy Shmaliy
Pages 425-517
9. Yuriy Shmaliy
Pages 519-588
10. Back Matter
Pages 589-639

### Introduction

Continuous-Time Systems is a description of linear, nonlinear, time-invariant, and time-varying electronic continuous-time systems. As an assemblage of physical or mathematical components organized and interacting to convert an input signal (also called excitation signal or driving force) to an output signal (also called response signal), an electronic system can be described using different methods offered by the modern systems theory. To make possible for readers to understand systems, the book systematically covers major foundations of the systems theory. First, the quantitative and qualitative methods of systems description are presented along with the stability analysis. The representation of linear time-invariant systems in the time domain is provided using the convolution, ordinarily differential equations (ODEs), and state space. In the frequency domain, these systems are analyzed using the Fourier and Laplace transforms. The linear time-varying systems are represented using the general convolution, ODEs, and state space. The nonlinear time-invariant systems are described employing the Taylor and Volterra series expansions, ODEs, state space, and approximate methods such as averaging, equivalent linearization, and describing function. Finally, the representation of nonlinear time-varying systems is given using the Taylor and Volterra series, ODEs, modulation functions method, and state space modelling. Review of matrix theory and other useful generalizations are postponed to Appendices.

### Keywords

Dirac delta function Electronic System Filter Linear Modulation Nonlinear Nonlinear system Phase Signal Simulation System Time-varying bifurcation modeling systems theory

### Editors and affiliations

• Yuriy Shmaliy
• 1
1. 1.Guanajuato UniversityMexico

### Bibliographic information

• Book Title Continuous-Time Systems
• Authors Yuriy Shmaliy
• DOI https://doi.org/10.1007/978-1-4020-6272-8
• Publisher Name Springer, Dordrecht
• eBook Packages Engineering Engineering (R0)
• Hardcover ISBN 978-1-4020-6271-1
• Softcover ISBN 978-90-481-7592-5
• eBook ISBN 978-1-4020-6272-8
• Edition Number 1
• Number of Pages XVIII, 640
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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## Reviews

From the reviews:

"This book is devoted to an introduction to the deterministic theory of continuous time systems described by ordinary differential equations. … The approach and the exposition are of the engineering level, without deeper mathematical developments. Many examples, mostly from electrical engineering, are presented. … the book is intended for electrical and electronic engineering students." (Tullio Zolezzi, Zentralblatt MATH, Vol. 1148, 2008)