Linear Continuous Time Systems
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Continuous-Time Systems
Author: Yuriy Shmaliy
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-09-23
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.
Discrete-Time Markov Jump Linear Systems
Author: O.L.V. Costa
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-03-30
Safety critical and high-integrity systems, such as industrial plants and economic systems can be subject to abrupt changes - for instance due to component or interconnection failure, and sudden environment changes etc. Combining probability and operator theory, Discrete-Time Markov Jump Linear Systems provides a unified and rigorous treatment of recent results for the control theory of discrete jump linear systems, which are used in these areas of application. The book is designed for experts in linear systems with Markov jump parameters, but is also of interest for specialists in stochastic control since it presents stochastic control problems for which an explicit solution is possible - making the book suitable for course use. From the reviews: "This text is very well written...it may prove valuable to those who work in the area, are at home with its mathematics, and are interested in stability of linear systems, optimal control, and filtering." Journal of the American Statistical Association, December 2005
Continuous-Time Signals and Systems (Version 2013-09-11)
This book is intended for use in teaching undergraduate courses on continuous-time signals and systems in engineering (and related) disciplines. It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been very well received by students. This book provides a detailed introduction to continuous-time signals and systems, with a focus on both theory and applications. The mathematics underlying signals and systems is presented, including topics such as: properties of signals, properties of systems, convolution, Fourier series, the Fourier transform, frequency spectra, and the bilateral and unilateral Laplace transforms. Applications of the theory are also explored, including: filtering, equalization, amplitude modulation, sampling, feedback control systems, circuit analysis, and Laplace-domain techniques for solving differential equations. Other supplemental material is also included, such as: a detailed introduction to MATLAB, a review of complex analysis, and an exploration of time-domain techniques for solving differential equations. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.