Week

TOPIC

ASSIGNED READING

HW and LAB Assigned

Notes

1 (1/8, 1/10)

Course introduction. Mathematical Description of Dynamic Systems. State space models. Model classification. Examples.

Chapter 1 

2 (1/15, 1/17)

Properties of linear systems. Zero-input and zero-state response. Relationship between SS and TF models.

Chapter 2

HW#1 

3 (1/22, 1/24)

Impulse response and convolution models. Linearization.

 Chapter 3

HW#2

4 (1/29, 2/1)

 Review of Linear Algebra. State transition matrix.

 Chapter 3, Appendix

5 (2/5, 2/7)

 Cayley-Hamilton theorem. Functions of square matrices and methods of their representation as a finite matrix polynomial series. Solution of LTI and LTV systems. State transition and fundamental matrices.

 Chapter 4

 HW#3

6 (2/12, 2/14)

 Properties of a state transition matrix. State space realizations and canonical forms. Jordan Canonical form and modal decomposition. Stability.

 Chapter 4

 HW#4

Lab#1

7 (2/19, 2/21)

Input-output and internal stability. Asymptotic, marginal and BIBO stability. Lyapunov (marginal) stability. Stability of LTV systems. 1^st Midterm

 Chapter 5

 HW5

8 (2/26, 2/28)

 Controllability, controllability Gramian, and controllability matrix.

 Chapters 6

HW6 

9 (3/4, 3/6)

 Kalman decomposition. Canonical realizations and transformations into canonical form: MIMO case

10 (3/11, 3/13)

 Balanced realization and balanced model reduction. Effect of discretization on controllability and observability.

11 (3/18, 3/20)

Spring Break

12 (3/25, 3/27)

 Pole placement methods. Bass-Gura fomula.

Chapter 6

 HW7

13 (4/1, 4/3)

Achermann's formula. Lyapunov equation approach. Selecting location of closed-loop poles. Tracking problem by pole placement. Introduction of the integral action.

 Chapter 7

14 (4/8, 4/10)

 Observers. Feedback based on state estimates

 Chapters 7 &8

 HW8

15 (4/15, 4/17)

2^nd Midterm. LQR

 Chapter 9

16 (4/22)

Kalman filter.

 Chapter 10 and 11