Linear control theory is a foundational subfield within control systems engineering focused on the analysis and design of dynamical systems whose behavior can be accurately approximated by linear differential equations. It investigates system stability, transient response, and steady-state performance using mathematical techniques such as Laplace transforms, frequency domain analysis, and state-space methods, leveraging the principle of superposition to provide a mathematically tractable framework for understanding and controlling a wide array of physical, biological, and economic processes.