Prof. J. Baillieul
Prof. T. Djaferis
Mechanical Engineering

Teaching Assistant
Henghui Zhu,
415, Photonics Bldg.

ENG ME/SE/EC 501: Dynamic Systems Theory — State-space linear systems

Course Outline: (Fall 2017)

  1. Mathematical preliminaries: linear algebra
    (i)  Finite dimensional linear spaces
    (ii)  Linear transformations and matrices
    (iii)  Jordan normal form

  2. State-space representation of linear control systems

  3. Mathematical foundations of state-space representations
    (i)  Existence and uniqueness results for linear ordinary differential equations
    (ii)  Peano-Baker series and matrix exponentials
    (iii)  Properties of the state-transition matrix

  4. Points of contract with frequency-domain analysis
    (i)  The resolvent; Newton’s algorithm
    (ii)  Stability analysis in the frequency domain

  5. Controllability and observability
    (i)   The controllability Grammian; the observability Grammian
    (ii)   Algerbaic tests for controllability and observability

  6. Shaping the dynamic response — Where do we put the closed-loop poles?
    (i)  Analysis of second-order systems; dc-motor control example
    (ii)  Design of regulators

  7. Digital control theory
    (i)   Modeling discrete-time and sampled-data systems
    (ii)   Analysis of sampled data systems

  8. Linear observers

  9. Compensator design by separation of variables principle

  10. Linear quadratic optimal control theoryl
    (i)  The Pontryagin maximum principle
    (ii)   Least squares theory and the matrix Riccati equation

  11. Random processes
    (i)   Wiener processes
    (ii)   The Ito calculus and the theory of stochastic differential equations
    (iii)   Recursive estimation

  12. Nonlinear/geometric control theory
    (i)   Introduction to the theory of differentiable manifolds
    (ii)   Accessibility, controllability, and system Lie algebras

  13. Suggested Reading

    Text: Roger W. Brockett, Finite Dimensional Linear Systems SIAM, 2015 / xvi + 244 pages / Softcover / ISBN 978-1-611973-87-7. For student discount prices, order according to the instructions given on the course web site.

    Previous text: Bernard Friedland, Control System Design: An Introduction to State-Space Methods, McGraw-Hill, 1986. Reissued by Dover Books on Engineering, 528 pages, Dover Publications (March 24, 2005), ISBN-10: 0486442780, ISBN-13:978-0486442785. Order online from: or

    Handy window for on-line price shopping:

    Other books:

    Panos J. Antsaklis & Anthony N. Michel, Linear Systems, ISBN: 0-07-041433-5, Electrical and Computer Engineering Series, McGraw-Hill, 1997, 696pages.

    Chi-Tsong Chen, Linear System Theory and Design, Oxford University Press, 3-rd Edition, ISBN 0-19511777-8, 1999, 334pages.

    Karl Johan ˚Astr¨om and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, ISBN-13: 978-0-691-13576-2, ISBN-10: 0-691-13576-2, 2008, 396 pages.

    Joao P. Hespanha, Linear Systems Theory, Princeton University Press, ISBN: 978-0-691-14021-6, 2009, 278 pages.

    Roger W. Brockett, Finite Dimensional Linear Systems, John Wiley and Sons, SBN 471 10585 6, 256 pages. (Out of print. See or download from course web site (


    Grades will be given for homework assignments (one every week or so), class participation, and one or two hour exams.

    For up-to-date information about the class, visit:
    For a downloadable PDF version of this syllabus, click

    (August 28, 2017)