Linear Systems

This textbook provides a mathematical introduction to linear systems, focusing on continuous-time models in engineering applications. It covers finite-dimensional state spaces, graphical methods, MIMO systems, orthogonal polynomials, infinite-dimensional Hilbert space, and modern applications to signal processing. The prerequisites are basic linear algebra and complex analysis.

Format: Hardback
Length: 410 pages
Publication date: 30 January 2023
Publisher: Springer International Publishing AG

This comprehensive textbook offers a thorough mathematical exploration of linear systems, with a particular emphasis on the continuous-time models that find applications in engineering fields like electrical circuits and signal processing. Through the use of block diagrams and the Laplace transform theory, the book provides a foundational understanding of linear systems, guiding readers through the complexities of complex analysis. The text primarily focuses on linear systems with finite-dimensional state spaces, presenting graphical methods such as Nyquist plots and Bode plots alongside computational tools like MATLAB. Additionally, it delves into the realm of multiple-input multiple-output (MIMO) systems, which are crucial in modern telecommunication devices. The book also introduces orthogonal polynomials, showcasing their significance in signal processing and wireless communication, with notable examples such as Telatar's model for multiple antenna transmission.

In the later chapters, the book extends its scope to infinite-dimensional Hilbert space, introducing the canonical model of a linear system. The final chapter explores contemporary applications of signal processing, including Whittaker's sampling theorem for band-limited functions and Shannons wavelet. Written with the guidance of experienced instructors, this textbook serves as a systematic and rigorous introduction to linear systems theory, making it invaluable for both undergraduate mathematics students and researchers in engineering. A solid foundation in basic linear algebra and complex analysis is assumed as prerequisites for this text.

Weight: 907g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031212390
Edition number: 1st ed. 2022