Synopses & Reviews
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.
Review
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)
Synopsis
This work offers students at all levels 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 to an output 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 the major foundations of the systems theory.
Table of Contents
1 Introduction. 1.1 Principles of Operation of Typical Systems. 1.2 Systems Performance and Classification. 1.3 Basic Structures. 1.4 Basic Operations with Signals in Systems. 1.5 Summary. 1.6 Problems. 2 Quantitative Methods of Systems Description. 2.1 System Responses to Test Signals. 2.2 Methods for Linear Systems. 2.3 Common Methods for Nonlinear Systems. 2.4 Approximation and Linearization. 2.5 Averaging. 2.6 Equivalent Linearization. 2.7 Norms. 2.8 System Stability. 2.9 Summary. 2.10 Problems. 3 Qualitative Methods of Systems Description. 3.1 Qualitative Analysis. 3.2 Phase Trajectories. 3.3 Bifurcations. 3.4 Chaotic Orbits and Fractals. 3.5 Conservative Systems. 3.6 Dissipative (Near Conservative) Systems. 3.7 Summary. 3.8 Problems. 4 LTI Systems in the Time Domain. 4.1 Introduction. 4.2 Convolution. 4.3 Presentation by Differential Equations. 4.4 Electric Circuit Presentation by ODEs. 4.5 System Simulation by Block Diagrams. 4.6 State-space Presentation. 4.7 Solution of State Space Equations. 4.8 Summary. 4.9 Problems. 5 LTI Systems in the Frequency Domain (Transform Analysis). 5.1 Introduction. 5.2 Fourier Analysis. 5.3 Laplace Transform. 5.4 Unilateral Laplace transform. 5.5 Applications of Laplace transform. 5.6 Stability Analysis of Feedback Systems. 5.7 Selective Filter Approximations. 5.8 Summary. 5.9 Problems 6 Linear Time-Varying Systems. 6.1 Introduction. 6.2 Time-varying Impulse Response and General Convolution. 6.3 Properties of LTV Systems. 6.4 Differential Equation Presentation. 6.5 State Space Presentation. 6.6 Linear Periodically Time-varying Systems. 6.7 Summary. 6.8 Problems. 7 Nonlinear Time Invariant Systems. 7.1 Introduction. 7.2 Memoryless Systems. 7.3 Presentation of Memory Systems by Volterra Series. 7.4 Representation in the Transform Domain. 7.5 Approximation by Describing Functions. 7.6 Description by Differential Equations. 7.7 State Space Presentation. 7.8 Summary. 7.9 Problems. 8 Nonlinear Time Varying Systems. 8.1 Introduction. 8.2 Memoryless Time-varying Nonlinearities. 8.3 Volterra Series Expansion. 8.4 Description by Differential Equations. 8.5 Nonlinear Periodically Time-varying Systems. 8.6 State-space Presentation. 8.7 Summary. 8.8 Problems. A Dirac Delta Function. B Matrices. C Tables of Fourier Series, Transform, and Properties. D Tables of Laplace Transform and Transform Properties. E Mathematical formulas. References. Index.