Linear Systems
Description
This book is about Linear Systems Theory, one of the most fundamental and important prerequisites necessary to study modern control techniques. Primarily intended for first-year graduate students (and advanced undergraduates) who are interested in the field of control, this book provides both a complete coverage of all standard linear systems concepts. More importantly, it extends these concepts through a smooth transition to the next level of control theory subfields, including nonlinear control, robust control, adaptive control, and stochastic control. The book achieves this by setting itself apart from many existing linear systems texts in two main ways. First, while many older texts remain influential, their ages also mean less connection to modern real-world applications, especially in rapidly evolving areas like data-driven control and autonomous control. Second, this book emphasizes the mathematical rigor foundational to control theory, offering a more complete understanding than texts that prioritize accessibility over depth. As readers will inevitably encounter such rigor and mathematical thinking while progressing through more advanced education, even in fields outside of controls, an earlier introduction to it is more favorable. This book is organized into four main parts: 1) linear system properties, 2) linear stability, 3) linear control and estimation, and 4) linear optimal control and estimation. The main chapters of this book are focused on presenting the essential ideas and tools needed to understand and apply linear systems, while reviewing all relevant preliminaries in a self-contained manner.
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Dr. SooJean Han is an Assistant Professor of Electrical Engineering at KAIST and the Director of the Autonomous Control for Stochastic Systems (ACSS) lab. Her interests lie broadly in the realm of combining model-based tools and data-driven AI for robust and adaptive control of stochastic systems. Her research spans a wide range of applications including motion-planning, distributed sensing and control, reinforcement learning, resource-allocation and scheduling, and decision-making for networks and multiagent systems. ACSS also maintains active collaborations with the AFOSR AOARD, the Agency for Defense Development (ADD) in Korea, as well as with faculty at KAIST, Seoul National University, and Kyung Hee University. As of 2025, Dr. Han and her team have published dozens of manuscripts in top-tier conferences (e.g., IEEE CDC, L4DC) and top-tier journals (Automatica, IJRNC, IEEE TAC). She has also developed and taught courses for a wide variety of subjects, including linear systems (for which this book is being written), probability and stochastic processes, optimal control, and stochastic control. She is currently serving as an Associate Editor in the IEEE RA-L journal, and has served in the past as an Associate Editor for IROS2025 and a Chair for CDC2024. Prior to KAIST, Dr. Han completed her Ph.D. in Control and Dynamical Systems at Caltech in Jan 2023, and was supported by the Caltech Special EAS Fellowship and the NSF GRFP. She received her B.S. in Electrical Engineering and Computer Science, and Applied Mathematics at UC Berkeley in 2016. She was also a research assistant in the Hybrid Systems Lab at UC Berkeley, and a research affiliate of Team CoSTAR for the DARPA subT Challenge at NASA JPL.
Content
I Linear System Properties.- 1.Introduction and System Definitions.- 2.Characteristic Modes.- 3.State-Transition Matrix.- II Linear Stability.- 1. Input-Output Stability.- 2. Internal Stability.- 3. Lyapunov Stability.- 4. Uniform Stability.- III Linear Control and Estimation.- 1. Canonical Forms.- 2. Minimum-Energy Input.- 3.Controllability.- 4.Observability.- 5. Minimal Realizations.- 6. Controller and Observer Design.- IV Linear Optimal Control and Estimation.- 1. Feedback Stabilization.- 2. The Linear Quadratic Regulator.- 3. Linear Robust and Stochastic Control.- 4 Linear State Estimation.