520.601 Introduction to Linear Dynamical Systems
Fall, 2005
Department of Electrical and Computer Engineering
Johns Hopkins University
Description
This is a beginning-graduate course in linear, time-invariant, single-input, single-output (SISO) systems.
Topics
- Continuous-time state equations (examples, state variable diagrams, variable changes, diagonal form).
- Linearization about constant operating points.
- Zero-input solution.
- Properties of matrix exponentials.
- Zero-state and complete solutions.
- LTI properties of solutions
- Discrete-time linear state equations and solution. (
-order difference
equation and sampled-data examples). - Laplace transform representation, solution formula, and further properties of matrix exponentials.
- Transfer functions, SISO response properties including steady-state frequency response and response characterizations of poles and zeros.
- Internal stability (asymptotic stability of zero-input response). (Eigenvalue and linear Lyapunov equation characterizations, but not Lyapunov stability.)
- External stability (BIBO stability of zero-state response).
- Discrete-time stability.
- Reachability and observability (including rank condition, PBH tests, and SISO canonical forms).
- Discrete-time case.
- Realization theory and minimal realization construction.
- Equivalence of asymptotic and BIBO stability.
- General properties of linear state/output feedback.
- Transfer function analysis of feedback: well posedness and internal stability.
- Stabilization and eigenvalue placement by state feedback (single-input case).
- Decoupling (noninteraction) by state feedback.
- State observers, both full and reduced dimension.
- Eigenvalue placement by dynamic output (observed state) feedback.
- Output regulation problem: asymptotic tracking of constant inputs with rejection of constant disturbances.
Prerequisites
Undergraduate courses in control systems and in linear algebra.
Instructor
Wilson J. Rugh , 205 Barton Hall
Email: rugh@jhu.edu
Office Hours: When my door is open, or by appointment
Text
None. The following books have been put on reserve at MSEL:
J.S. Bay, Fundamentals of Linear State Space Systems, McGraw Hill, 1999.
J.D. Aplevich, Essentials of Linear State Space Systems, Wiley, 1999.
C.T. Chen, Linear System Theory and Design, 3rd edition, Oxford, 1999.
Schedule
MTW 2, 117 Barton Hall
Final Exam: 1pm, December 19 in 117 Barton Hall
The final exam and course grade can be picked up in the ECE office, 105 Barton Hall, after 9am, Wednesday, December 21.(The course grade is based on the sum of the exam scores plus 0.9 times the total of homework scores, after droppping one.)
Homework
In a graduate course such as this, homework should be an individual effort. On the other hand, students should be encouraged to discuss the course material and help each other with obscurities and difficulties. The following policy is an attempt to fairly delineate the boundaries of homework collaboration. Discussion of particular aspects of the homework assignment is permitted for clarification of the problems, but no notes should be carried away from the discussion. The written work you hand in should be your own work.
Be extremely neat, precise, and concise. It is important that you learn what to include and what to omit from your solutions. Staple your homework in the upper left corner, and begin each problem, in correct order, at the top of a new page (or side). (Sorry about the trees.)
All of the problems that will be assigned can be solved using material that we have discussed in class. Do not solve a problem by quoting a theorem in some reference, or by stating that the solution is an easy consequence of Theorem 5.5 in a book you found. All problems can and should be solved using the approaches and tools we have discussed in class.
Homework Assignments
Homework 4 Please ignore the duplicate problem!