This book presents recent developments in two-dimensional (2-D) linear system theory. It covers various aspects of 2-D systems, including state-space models, transfer function matrices, controllability and observability, stability and stabilization, characteristic polynomial and eigenvalue assignment, and deadbeat control and servo problems. The book is organized into seven chapters, each focusing on different aspects of 2-D systems. Chapter 1 introduces different state-space models for 2-D systems, including Roesser's model, Attasi's model, and two Fornasini-Marchesini models. It discusses the transition matrices and general response formulas for these models. Chapter 2 focuses on the transfer function matrix and realization problem. It covers the transfer function matrix of different models, matrix fraction description, proper transfer function matrices, and the realization problem. Chapter 3 discusses controllability and observability of 2-D systems, including local controllability and observability, separate local controllability and observability, modal controllability and observability, and the separability of transfer function matrices. It also covers minimum energy control. Chapter 4 addresses stability and stabilization of 2-D systems, including the stability of 2-D linear input-output systems, stability of Roesser's model, asymptotic and exponential stability of Fornasini-Marchesini's models, margin of stability, and stabilization of 2-D systems by state or output feedback. Chapter 5 discusses characteristic polynomial and eigenvalue assignment, including coefficient assignment methods, characteristic polynomial assignment, dynamic output feedback, PID controllers, and eigenvalue assignment. Chapter 6 covers asymptotic and deadbeat observers, exact model matching, and decoupling. Chapter 7 presents new results concerning deadbeat control and deadbeat servo problems, including polynomial design of deadbeat control laws, output deadbeat control, deadbeat control of closed-loop and open-loop systems, and deadbeat servo problems for single-input single-output and multivariable linear systems. An appendix provides basic definitions, theorems, and computational algorithms for 2-D systems. The book is intended for graduate students, scientists, engineers, and mathematicians interested in control theory and applications.This book presents recent developments in two-dimensional (2-D) linear system theory. It covers various aspects of 2-D systems, including state-space models, transfer function matrices, controllability and observability, stability and stabilization, characteristic polynomial and eigenvalue assignment, and deadbeat control and servo problems. The book is organized into seven chapters, each focusing on different aspects of 2-D systems. Chapter 1 introduces different state-space models for 2-D systems, including Roesser's model, Attasi's model, and two Fornasini-Marchesini models. It discusses the transition matrices and general response formulas for these models. Chapter 2 focuses on the transfer function matrix and realization problem. It covers the transfer function matrix of different models, matrix fraction description, proper transfer function matrices, and the realization problem. Chapter 3 discusses controllability and observability of 2-D systems, including local controllability and observability, separate local controllability and observability, modal controllability and observability, and the separability of transfer function matrices. It also covers minimum energy control. Chapter 4 addresses stability and stabilization of 2-D systems, including the stability of 2-D linear input-output systems, stability of Roesser's model, asymptotic and exponential stability of Fornasini-Marchesini's models, margin of stability, and stabilization of 2-D systems by state or output feedback. Chapter 5 discusses characteristic polynomial and eigenvalue assignment, including coefficient assignment methods, characteristic polynomial assignment, dynamic output feedback, PID controllers, and eigenvalue assignment. Chapter 6 covers asymptotic and deadbeat observers, exact model matching, and decoupling. Chapter 7 presents new results concerning deadbeat control and deadbeat servo problems, including polynomial design of deadbeat control laws, output deadbeat control, deadbeat control of closed-loop and open-loop systems, and deadbeat servo problems for single-input single-output and multivariable linear systems. An appendix provides basic definitions, theorems, and computational algorithms for 2-D systems. The book is intended for graduate students, scientists, engineers, and mathematicians interested in control theory and applications.