20 Best Books on Linear Systems

Book Review: This book provides a balanced approach to understanding and applying linear system theory and design. It presents concepts and design techniques in a simple and practical manner, making it easy for students to grasp. It is suitable for both graduate and undergraduate courses on linear systems and multivariable system design. The book covers important topics such as state space equations and their real-time processing, rational transfer functions, and provides a historical overview of linear system theory and design.

Book Review: This textbook is a good choice for students studying differential equations at the graduate and undergraduate level. It not only covers the theoretical aspects of dynamical systems but also helps students develop their mathematical skills to analyze different types of differential equations. The author includes numerous exercises and examples, particularly focusing on linear systems of differential equations. The book also features updated material and expanded applications that are relevant to real-world studies and practical applications.

Book Review: This book serves as an introductory guide to state space methods, which are essential for analyzing and designing linear control systems. It is highly valuable not only for practicing engineers and researchers but also for students pursuing advanced studies in systems and control theory. The book begins by introducing the fundamental principles of state space methods and subsequently offers rigorous mathematical treatment of the underlying concepts and theoretical findings. With chapters dedicated to state space fundamentals, controllability, observability, stability, minimal realizations, optimal control, and more, the book covers a wide range of topics in depth.

“Analysis and Design of Descriptor Linear Systems” Book Review: This book offers an introductory overview of the theory of descriptor linear systems, covering both fundamental and advanced concepts, as well as recent developments in the field. It provides a detailed explanation of algorithms used for the analysis and solution of design problems. To enhance understanding, the book includes numerous examples, references, and appendices. It serves as a valuable resource for practitioners and theoreticians working in the field of linear systems.

“Well-Posed Linear Systems” Book Review: This book provides description of well-posed infinite-dimensional linear systems that incorporate input, state, and output variables simultaneously. It specifically explores a class of non-well-posed systems arising from system nodes. The book includes the latest findings in the field of linear systems, making it a valuable resource for students, professionals, and researchers specializing in systems theory, operator theory, delay equations, and partial differential equations.

“Time-Varying Discrete Linear Systems” Book Review: This book provides an extensive overview of discrete-time systems with time-varying coefficients. It covers various topics, including discrete-time nodes, the discrete counterpart of the continuous case, discrete-time Lyapunov and Riccati equations, and the connection between discrete-time Hamiltonian systems and input-output operators, along with associated Hankel and Toeplitz operators. The concepts and tools presented in this book are essential for addressing stabilization and disturbance attenuation problems. The book focuses on recent advancements in the field of discrete-time systems and linear systems.

“Max-Linear Systems: Theory and Algorithms” Book Review: This book provides an introduction to the fundamental principles of max-algebra. Each chapter explores various topics, including max algebraic theory, linear algebra, algorithms and algorithmic problems, max-linear systems, the eigenvalue-eigenvector problem, periodic behavior of matrices, max-linear programs, linear independence, and matrix scaling. Theoretical concepts and practical applications of max-linear systems in diverse fields are illustrated throughout the book. Numerous examples, numerical exercises, and recent research findings are included to enhance understanding. While primarily intended for graduating students and mathematics researchers, the book also offers valuable insights for mathematicians working in industry, commerce, or management.

“Stability and Stabilization of Linear Systems with Saturating Actuators” Book Review: This book is highly beneficial for electrical, mechanical, chemical, and aeronautical engineers engaged in control applications. It serves as a useful reference for graduate students and researchers involved in the advancement of tools and theoretical results in various fields of control applications, specifically focusing on systems with saturation. The book provides presentation of both fundamental concepts and essential tools for the analysis and synthesis of linear systems incorporating actuator saturation. It addresses stability analysis and the synthesis of stabilizing control laws, considering both local and global conditions. Stability and stabilization conditions are illustrated using Lyapunov, polyhedral, quadratic, and Lure-type functions, covering both internal and external stability. The book presents an anti-windup approach to solve problems and mitigate the undesirable effects of saturation. It incorporates recent research, developments, and numerous results in the field of linear systems with saturating actuators.

“Fundamentals of Linear Systems for Physical Scientists and Engineers” Book Review: The book introduces fundamental concepts and principles of linear systems, drawing inspiration from various engineering and physical science disciplines. The chapters cover a wide range of topics, including linear continuous systems, discrete-time systems, stochastic processes, Lyapunov functions, and stability conditions for equilibrium solutions. The content of the book is highly practical and applicable to various engineering domains. It includes a significant number of original proofs, examples, and proven theorems to effectively demonstrate and analyze the presented material.

“Linear Systems and Operators in Hilbert Space” Book Review: The book explores system theory in the context of infinite-dimensional spaces. It discusses the mathematical foundations of system theory, employing advanced techniques from operator theory in Hilbert spaces and invariant subspaces. The topics covered include linear algebra, finite-dimensional systems, operators in Hilbert space, linear systems in Hilbert space, the structure of self-adjoint and unitary transformations, and the structure of restricted shift operators. The book includes numerous examples, problems, references, and notes.

“Nonlinear Control Systems and Power System Dynamics” Book Review: This book offers a detailed explanation of the concepts, theorems, and algorithms in nonlinear control theory, accompanied by step-by-step examples. It specifically focuses on the application of nonlinear control theory to electric power systems, providing a thorough description of the nonlinear control techniques employed. The book serves as an ideal text for senior undergraduate and graduate engineering students studying control theory, while also serving as a valuable reference for control theory researchers, engineers, and researchers interested in the application of modern nonlinear control theory. The contents of the book cover a range of topics, including the basic concepts of nonlinear control theory, design principles for single-input single-output and multi-input multi-output nonlinear control systems, fundamental mathematical descriptions for electric power systems, and nonlinear control techniques for specific power system components such as synchronous generators, steam valves, HVDC systems, static Var systems, and robust control of power systems.

“Nonlinear Dynamics and Complexity (Nonlinear Systems and Complexity)” Book Review: This book offers an exploration of current trends in nonlinear dynamics, covering a wide range of topics such as analytical solutions, Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. By discussing Nonlinear Dynamics and Complexity, the book aims to enhance the understanding of the mechanisms and phenomena within nonlinear dynamics and develop the corresponding mathematical theory to apply nonlinear design in practical engineering applications. The contents of the book encompass various subjects, including Long Range Order to Complex Networks, a Hamiltonian Dynamics Perspective, Time-Varying Linearization, the Perron Effects of Lyapunov Exponent Sign Inversion, Stability and Instability by the First Approximation, Fractional Maps as Maps with Memory, Complex Period, Motion in a Periodically Forced Quadratic Nonlinear Oscillator, a Map-Based Approach to Problems of Spiking Neural Network Dynamics, an Adaptive Landscape with Singularity in Biological Processes, Multiscale Scaffolding of Real World Data, and Treasure Hunting in Virtual Environments.

“Nonlinear Dynamics New Directions (Nonlinear Systems and Complexity)” Book Review: This book discusses various concepts, such as fractal analysis and the specific applications of dynamical systems theory in biology. With a primary focus on the novel applications of dynamical systems theory in both engineering and biology, this volume explores recent advancements, including large deviations for higher-dimensional maps, investigations of measures resisting multifractal analysis, and an overview of complex Kleinian groups. The topics covered in this volume focus fluctuations in dynamical systems, fractal analysis, studies on the transient dynamics of biological networks, synchronization in lasers, control of chaotic systems, and more. The book includes a review of recent findings that highlight exciting prospects for future development.

“System Dynamics” Book Review: This textbook covers various concepts, including the initial steps in modeling a dynamic system and the development of mathematical models necessary for feedback control, among others. It provides a well-rounded combination of fundamental information essential for mechanical engineers. The book focuses on the fundamental theoretical development rather than relying on the application of commercial software. To engage students who may not have a strong mathematical background, the author has also incorporated practical details of machine design. The contents of the book span topics such as differential equations, input functions, complex exponentials, transfer functions, the linear graph method, step responses, superposition, mechanical systems, fluid, electrical, and thermal systems, power transmission, transformation and conversion, vector-matrix algebra, the state-space representation of dynamic systems, finite difference methods, MATLAB, and transfer functions.

“Linear Systems Analysis” Book Review: This textbook serves as a resource for the introductory course in Linear Systems Analysis, specifically tailored for students in Electrical, Electronics, and Computer Engineering. It places a strong focus on cultivating a conceptual understanding of the modeling process for physical systems and the various techniques employed in their analysis. The book features a wide range of exercises designed to enhance students’ analytical skills. It covers the fundamental principles and techniques essential for modeling, analyzing, and simulating linear dynamic systems. Successful completion of this course is a prerequisite for advanced studies in Control Systems, Network Theory, Communications, and related subjects.

“Network Analysis and Synthesis (Including Linear System Analysis)” Book Review: This textbook is specifically designed for undergraduate students majoring in electrical, electronics, communication, and computer engineering. It provides coverage of both fundamental concepts and more advanced topics in the field. The book begins with the basics, including circuit elements, Kirchhoff’s laws, network equations, and resonance. It then progresses to relatively advanced subjects such as modern filters, state variable analysis, active RC filters, and sensitivity considerations. With a total of 16 chapters, the book offers a balanced mix of theory and practical application. It features numerous solved examples and practice problems to reinforce understanding. It includes over 500 multiple-choice questions at the end of the book to test and assess knowledge. The topics covered in this textbook span a wide range, including basic circuit elements, network theorems, network equations, differential equations, graph theory, Fourier series, Fourier transforms, Laplace transform, network functions, and resonance. The book also discusses advanced subjects like passive network synthesis, state variable analysis, analogous systems, attenuators, classical filters, modern filter theory, active RC filters, frequency response, Bode plot, and z-transforms, providing detailed explanations and insights into these areas of study.

“Linear Systems: Analysis and Applications” Book Review: This book explores a wide range of essential topics in Linear Systems. It offers a plethora of solved and unsolved problems, review questions, and multiple-choice questions to enhance learning and understanding. The contents of the book cover various important areas. It begins by introducing discrete systems and their analysis, including the use of Z-transformations. It focuses on the analysis and applications of Fourier series and Fourier transforms. The book also explores network functions and synthesis, utilizing Laplace transforms and their practical applications. The book provides an introduction to discrete-time control systems and delves into the analysis of continuous and discrete-time systems using state space methods. The importance of discrete transform analysis is also discussed. Throughout the book, the author provides detailed explanations and examples to facilitate comprehension and application of the concepts. This book serves as a valuable resource for students and practitioners studying Linear Systems.

“Analysis Of Linear Systems” Book Review: This book is designed to provide valuable assistance to undergraduate students studying Electrical and Electronics Engineering. It encompasses a wide range of important concepts, including the characteristics of linear systems, classical solutions of linear differential equations, lumped-element electrical systems, analogous systems, analysis using Fourier methods, the Laplace transformation, applications of Laplace transformations, additional concepts and theorems, systems with feedback, sampled-data systems, the Z transformation, systems with distributed parameters, numerical solution of algebraic equations, and tables of Laplace transforms. To enhance the learning experience, the book also includes answers to problems and offers practice exercises for students to reinforce their understanding of the material. This book serves as a valuable resource for undergraduate students in the field of Electrical and Electronics Engineering.

“Nonlinear Systems” Book Review: This textbook is specifically designed for a first-year graduate-level course on nonlinear systems, making it an excellent resource for students pursuing advanced studies in engineering and applied mathematics. However, it can also be utilized for self-study or as a reference by professionals in these fields. The book is divided into four parts, namely Basic Analysis, Analysis of Feedback Systems, Advanced Analysis, and Nonlinear Feedback Control. Each part provides coverage of its respective topic, accompanied by detailed explanations to facilitate a thorough understanding of the subject matter.