ENAE 641: Linear System Dynamics, University of Maryland, Dept. of Aerospace Engineering, Fall 2026 (Tue/Thu 12:30-13:45).
Overview
- A practical introduction to the theory of multivariable, linear dynamical systems and feedback control design
- The material is a fundamental building block for a graduate program in aerospace control systems
NOTE
- The header of the grading-policy handout reads “ENAE 641: Estimation and Control of Stochastic Systems”; the topical outline (and the course itself) is “ENAE 641: Linear System Dynamics”
Instructor
| Instructor | Prof. Rob Sanner |
| Office | EGR-3186 |
| [email protected] | |
| Website | ELMS (elms.umd.edu) |
| Office hours | T/Th 4-6 (via Zoom) |
Grading
| Component | Weight |
|---|---|
| 6-7 problem sets | 20% |
| 2 midterm exams | 65% |
| 1 final project | 15% |
- Grades are based on the overall weighted average:
- : A
- -: B
- -: C
- / boundaries at equally spaced divisions within these ranges
- Nominally no curve on raw scores (may be revisited if scores show an unusually low distribution)
Textbooks
- No required texts: everything needed for the assignments and exams is in the course notes
- Additional references, in rough order of utility:
- Hespanha, J., Linear Systems Theory, 2nd ed., ISBN 0691179575 (optional/recommended text)
- Chen, C., Linear Systems Theory and Design, 3rd ed., ISBN 0195117778
- Skogestad, S. and Postlethwaite, I., Multivariable Feedback Control, ISBN 0471943304
- Rugh, Linear System Theory, 2nd ed., Prentice Hall, 1996
- Maciejowski, Multivariable Feedback Design, Addison Wesley, 1990
Homework and Exam Policies
- Discussing problem sets in groups is encouraged (a proven, effective way to learn), but all submitted material, including any computer code, must be your own unique work
- Homework is usually due on Gradescope 7-10 days after it is posted on ELMS
- Solutions are normally on ELMS about a week after the due date
- Late homework: flat 15% penalty, accepted only until the solution is distributed
- Midterms are in class, at the regular class time; dates announced in class (expected roughly mid-October and end of November)
- The final project is take-home, due before the end of final exam week
Topical Outline
- In rough chronological order:
- Linearization of nonlinear systems; linear state space models
- Fundamental solutions, state transition matrix, general solution
- Linear vector spaces; linear algebra review
- LTI matrix exponential; eigenstructure analysis; modal decompositions
- Stability of linear systems; Lyapunov stability criteria
- Input/output stability
- Controllability and Observability; Gramians
- Coordinate transforms and canonical forms
- LTI singular value decompositions; multivariable frequency response
- Full state feedback techniques; pole placement
- Linear Quadratic Regulators (optimal state feedback)
- State Observers
- Observer/Controller designs; separation principle
- Canonical servo loop and MIMO compensators
- Tracking; disturbance and noise rejection
- The Continuous Kalman Filter; LQG compensators
- “Loop shaping” augmentation/tuning for LTI performance and robustness
- Introduction to design
Notes So Far
- Conventions: Notation
- Models: State-Space Models, Linearization, Equilibria and Trim Conditions
- Linear algebra: Linear Vector Spaces, Matrix Algebra, Range, Rank, and Nullspace, Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem, Vector and Matrix Norms, Quadratic Forms
- Solutions: Fundamental Matrix, State Transition Matrix, General Solution of the State Equation, Matrix Exponential, Resolvent Matrix, Transfer Function Matrix
- Eigenstructure and coordinates: Dyadic Expansion, Modal Decomposition, State Coordinate Transformations, Jordan Normal Form, Lyapunov Transformations, Floquet Theory
- Stability: Internal Stability, Lyapunov Functions, Lyapunov Equation, Local Stability