This course introduces the basic principles and tools for the design and analysis of feedback systems. It is intended to serve a diverse audience of scientists and engineers who are interested in understanding and utilizing feedback in physical, biological, information and social systems. A major goal of this course is to present a concise and insightful view of the current knowledge in feedback and control systems. In developing this course, we have attempted to condense the current knowledge by emphasizing fundamental concepts. We believe that it is important to understand why feedback is useful, to know the language and basic mathematics of control and to grasp the key paradigms that have been developed over the past half century. It is also important to be able to solve simple feedback problems using back-of-the-envelope techniques, to recognize fundamental limitations and difficult control problems and to have a feel for available design methods.Topics include: Introduction and course overview – automatic control, why and where is it used (examples) overview of main concepts: feedback vs. open loop control, performance measures, analogue and digital control. Laplace transforms – review of methods and standard results, especially the solution of linear differential equations, transfer functions, block diagrams. Dynamic modeling and model properties - differential equations, transfer functions, state-space forms of system models; conversion between types; block diagrams and prototype feedback control systems, performance metrics, standard first-order and second-order systems, impulse and step responses, effect of poles and zeros, steady-state error. PID control – definition, effects of the proportional, integral and derivative terms, choice of gains in simple cases, Ziegler-Nichols methods. Root locus methods – characteristic equation, definition of the root locus (RL), rules for sketching the RL, control system design using root locus techniques, lead and lag compensators, Matlab RLTOOL, pre-compensators and sensitivity function. Frequency response methods – frequency response function, Bode plots, Nyquist plots, stability conditions, gain and phase margins, relative stability, M-circles, lead/lag compensator designs. State-space control – stability, full state feedback, controllability, control canonical form, pole placement, state observer, observer canonical form and placement of observer poles, introduction to linear optimal control. The course makes wide use of Matlab to represent and simulate control systems. A group final project on control system design is included in the course; this makes use of Matlab and Simulink for simulation and design.