Linear Dynamic Systems and Signals
The author's twelve years of experience with linear systems and signals are reflected in this comprehensive book. The book contains detailed linear systems theory essentials. The intent of this book is to develop the unified techniques to recognize and solve linear dynamical system problems regardless of their origin. Includes Space state techniques as the time domain approach for studying linear systems. Provides a solid foundation on linear dynamic systems and corresponding systems using the dynamic system point of view. Parallels continuous- and discrete-time linear systems throughout to help users grasp the similarities and differences of each. Three part organization: Part I covers frequency-domain approach to linear dynamic systems, Part II covers the time-domain approach to linear dynamic systems, and Part III discusses the linear system approach to electrical engineering, to allow the user to focus of the subject matter as it pertains to their needs. For anyone interested in linear systems and signals
Why Read This Book
You should read this book if you want a rigorous, unified treatment of linear dynamical systems that ties frequency‑domain methods (Laplace/Z/DTFT) to time‑domain state‑space analysis for both continuous and discrete cases. It will give you the theoretical tools to model, analyze, and reason about linear systems you encounter in DSP, control, and signal processing.
Who Will Benefit
Advanced undergraduates, graduate students, and practicing engineers who need a solid mathematical foundation in linear systems theory to analyze and design filters, state‑space models, and stability tests.
Level: Advanced — Prerequisites: Single‑variable calculus, basic complex variables, linear algebra (eigenvalues/eigenvectors, matrix algebra), and an introductory familiarity with signals and systems (convolution, transforms).
Key Takeaways
- Analyze LTI systems using Laplace, Z, DTFT/FT and relate frequency‑domain results to time‑domain behavior.
- Model physical and signal processing systems in state‑space form and derive closed‑form solutions of state equations.
- Assess stability using eigenvalue/location tests and Lyapunov methods for continuous and discrete systems.
- Determine controllability and observability and compute minimal realizations and canonical forms.
- Convert between continuous and discrete representations via sampling and discretization methods.
- Apply modal decomposition and realization theory to design and analyze linear filters and system responses.
Topics Covered
- Part I: Frequency‑Domain Methods — Laplace Transform and Continuous‑Time Frequency Analysis
- Z‑Transform, DTFT and Discrete‑Time Frequency‑Domain Methods
- System Functions, Poles and Zeros, and Frequency Response
- Convolution, Impulse Response, and Transfer Function Techniques
- Part II: State‑Space Fundamentals — State Equations and Solutions
- Matrix Exponentials and Modal Analysis
- Controllability, Observability, and Minimal Realizations
- Canonical Forms and Realization Theory
- Stability Analysis: Eigenvalues, Routh/Hurwitz, and Lyapunov Methods
- State Feedback, Observers, and Basic Controller Concepts
- Sampling, Discretization, and Interplay Between Continuous and Discrete Models
- Special Topics: Descriptor Systems, Multivariable Systems, and Structured Realizations
- Appendices: Mathematical Background and Transform Tables
How It Compares
Covers similar foundational ground to Chen's "Linear System Theory and Design" and Kailath's "Linear Systems", but Gajic emphasizes a unified continuous/discrete presentation with strong links to frequency‑domain techniques useful for DSP engineers.
