Theory and Design of Control Systems


Credit Hours:


Learning Objective:

This course is designed to provide a graduate level introductory treatment of the theory and design of linear feedback control systems from both classical and modern viewpoints, with a strong emphasis on the design of performance-oriented controllers under typical practical implementation constraints. Such a goal will be achieved through the understanding of fundamental performance limitations of various control architectures and the integration of state-space design methodologies with their frequency domain interpretations.


This course will be divided into two parts. The first part will have an emphasis on single-input single-output (SISO) control in the classical sense, i.e. with an emphasis on modeling, analysis, and control design in the frequency domain. Advanced mathematical design tools will be introduced to formalize the underlining design principles of these classical design methodologies, with a strong emphasis on the understanding of fundamental performance limitations of various controller architectures. The second half of this course will focus on modern control theory, with an emphasis on modeling, analysis, and control design in the state-space domain. Throughout the course we will work almost entirely with linear systems, and we will draw meaningful connections between frequency and time-domain based approaches to control engineering. Fall 2020 Syllabus

Topics Covered:

Modeling: transfer function and state-space representations of differential governing equations; time and frequency-domain system response.
Analysis: stability of linear and nonlinear systems; nominal sensitivity functions;Nyquist stability criterion; stability margins; sensitivity, robustness, and the robust stability theorem; design specifications and characterization of constraints; effect of open-loop integrators, poles and zeros; frequency-domain design limitations; eigenvalue and eigenvectors; Jordan canonical form; controllability and stabilizability; observability and detectability; canonical decomposition.
Design: pole placement techniques in both the frequency domain and via state feedback; full state and reduced-order observer design; output feedback design; transfer function interpretations of output feedback design; introduction to the linear quadratic regulator.


Undergraduate level introductory control course (e.g. ME 475) and willingness of student to study the materials on own for any missing background needed. For the standard material covered in the undergraduate control course, please refer to (the digital control part is not needed).

Applied / Theory:

50 / 50

Web Address:

Web Content:

Syllabus, grades, lecture notes, homework assignment and solutions.


Regularly assigned homework.




One midterm exam and one final exam.


Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Textbook: Feedback Systems: An Introduction for Scientists and Engineers, Karl J. ??str??m and Richard M. Murray, 2nd Ed. (available on-line) Lecture notes will be posted to the course website Recommended Reference: Multivariable Feedback Control: Analysis and Design, Sigurd Skogestad and Ian Postlethwaite, Wiley, 2nd Ed., 2005. (paperback version)

Computer Requirements:

ProEd minimum computer requirements; MATLAB Robust Control Toolbox with version 3.0 or higher (student version of Matlab can be accessed via Purdue GoRemote - (, Matlab details can be found at the website of The Mathworks, Inc.

Other Requirements:

It is strongly advised that you go through the Matlab tutorial at

ProEd Minimum Requirements: