EE142: Linear Systems: State-Space Approach (Winter 2014)

Catalog description

State-space methods of linear system analysis and synthesis, with application to problems in networks, control, and system modeling.

Course webpage

See courseweb for further class materials and information. This course will not be hosted on eeweb. The syllabus can be found here.

Organization

Lecture times & location

Tuesday 12:00pm–1:50pm in 9436 Boelter Hall
Thursday 12:00pm–1:50pm in 9436 Boelter Hall

Discussion times & location

Wednesday 4:00pm–4:50pm in 5264 Boelter Hall
Friday 2:00pm–2:50pm in 4413 Boelter Hall

Contact information and office hours

  • Instructor:
    Florian Dörfler
    Email: dorfler@seas.ucla.edu
    Office location: 6730D Boelter Hall
    Tentative office hours: Wednesday 1:00pm–3:00pm

  • Teaching assistant:
    Chung-Kai Yu
    Email: ckyuna@ucla.edu
    Office location: Eng IV 67112
    Tentative office hours: Monday 2:00pm–4:00pm

Grading policy

15% homework, 10% project, 25% midterm, 50% final

Text(s)

A set of self-contained set of notes will be provided. Additionally, we will make use of the following textbook:

Feedback Systems: An Introduction for Scientists and Engineers, Karl J. Aström and Richard M. Murray, Princeton University Press, 2010.

The book is freely available at the second author's website: www.cds.caltech.edu/~murray/amwiki/.

Academic integrity

All standard HSSEAS academic integrity guidelines apply.

Topics covered in the course and tentative level of coverage

  • Mathematical models of physical systems in the form of ordinary differential equations and difference equations, examples. [2 hours]

  • Solutions of linear ordinary differential and difference equations with constant coefficients. [2 hours]

  • Mathematical background on linear algebra: vector spaces, basis, linear transformations and their matrix representations, eigenvectors, eigenvalues and singular values of linear transfor- mations, simple linear transformations. [5 hours]

  • Linear dynamic systems described by ordinary differential and difference equations and their matrix representations with respect to a given basis, state transition matrix and its properties. [6 hours]

  • Linear time-invariant dynamic systems, matrix exponential and its computation, canonical forms, modal representations, dominant modes, transfer functions. [4 hours]

  • Controllability, observability of linear continuous and discrete-time systems and their canonical forms. [6 hours]

  • Introduction to observers. [2 hours]

  • Stability of linear time-invariant continuous and discrete-time systems. [2 hours]

  • Feedback stabilization of linear time-invariant continuous and discrete-time systems. [1 hour]