6.241
Dynamic Systems and Control
Spring 2011
Topics
- Introduction to dynamic systems and control, matrix algebra
- Least squares error solutions of overdetermined / underdetermined systems
- Matrix norms, SVD, matrix perturbations
- Matrix perturbations
- State-space models, linearity and time invariance
- Solutions of state-space models
- Similarity transformations, modes of LTI systems, Laplace transform, transfer functions
- Stability, Lyapunov methods
- External I/O stability, storage functions
- Interconnected systems, feedback, I/O stability
- System norms
- Performance measures in feedback control
- Small gain theorem, stability robustness
- Stability robustness (MIMO)
- Reachability
- Reachability: standard and canonical forms, modal tests
- Observability
- Minimality, realization, Kalman decomposition, model reduction
- State feedback, observers, output feedback, MIMO poles and zeros
- Minimality of interconnections, pole/zero cancellations
- Parameterization of all stabilizing controllers
- Optimal control synthesis: problem setup
- H 2 optimization
- H ∞ optimization
Readings
- Luenberger, David. Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley, 1979. ISBN: 9780471025948.
- Kailath, Thomas. Linear Systems. Prentice Hall, 1980. ISBN: 9780135369616.
- Doyle, John, Bruce Francis, and Allen Tannenbaum. Feedback Control Theory. Dover, 2009. ISBN: 9780486469331.
- Vaccaro, Richard. Digital Control: A State-Space Approach. McGraw-Hill, 1995. ISBN: 9780070667815.
- Course notes are courtesy of Mohammed Dahleh, Munther A. Dahleh, and George Verghese, and are used with permission. Chapters 9, 16 and 23 are not available on MIT OpenCourseWare.
- CHAPTER #: 9 · TOPICS: [topic not available]
- CHAPTER #: 16 · TOPICS: System norms
- CHAPTER #: 23 · TOPICS: CT reachability, canonical forms
- LEC #: 1 · LECTURE TOPICS: Introduction to dynamic systems and control, matrix algebra · READINGS: Chapter 1
- LEC #: 2 · LECTURE TOPICS: Least squares error solutions of overdetermined / underdetermined systems · READINGS: Chapters 2 and 3
- LEC #: 3 · LECTURE TOPICS: Matrix norms, SVD, matrix perturbations · READINGS: Chapter 4
- LEC #: 4 · LECTURE TOPICS: Matrix perturbations · READINGS: Chapter 5
- LEC #: 5 · LECTURE TOPICS: State-space models, linearity and time invariance · READINGS: Chapters 6–8
- LEC #: 6 · LECTURE TOPICS: Solutions of state-space models · READINGS: Chapters 10 and 11
- LEC #: 7 · LECTURE TOPICS: Similarity transformations, modes of LTI systems, Laplace transform, transfer functions · READINGS: Chapter 12
- LEC #: 8 · LECTURE TOPICS: Stability, Lyapunov methods · READINGS: Chapters 13 and 14
- LEC #: 9 · LECTURE TOPICS: External I/O stability, storage functions · READINGS: Chapter 15
- LEC #: 10 · LECTURE TOPICS: Interconnected systems, feedback, I/O stability · READINGS: Chapters 15 and 17
- LEC #: 11 · LECTURE TOPICS: System norms · READINGS: Chapter 16
- LEC #: 12 · LECTURE TOPICS: Performance measures in feedback control · READINGS: Chapter 18
- LEC #: 13 · LECTURE TOPICS: Small gain theorem, stability robustness · READINGS: Chapter 19
- LEC #: 14 · LECTURE TOPICS: Stability robustness (MIMO) · READINGS: Chapters 20 and 21
- LEC #: 15 · LECTURE TOPICS: Reachability · READINGS: Chapter 22
- LEC #: 16 · LECTURE TOPICS: Reachability: standard and canonical forms, modal tests · READINGS: Chapter 23
- LEC #: 17 · LECTURE TOPICS: Observability · READINGS: Chapter 24
- LEC #: 18 · LECTURE TOPICS: Minimality, realization, Kalman decomposition, model reduction · READINGS: Chapter 25
- LEC #: 19 · LECTURE TOPICS: State feedback, observers, output feedback, MIMO poles and zeros · READINGS: Chapters 26–29
- LEC #: 20 · LECTURE TOPICS: Minimality of interconnections, pole/zero cancellations · READINGS: Chapter 30
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW syllabus ↗
- MIT OCW readings ↗
- MIT OCW calendar ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.