Course Structure

The following subjects are studied in the class to meet the course goals and learning objectives:

Topic	Number of Lectures
Dynamics and Feedback	4
Dynamics of Linear Systems	13
Full State Feedback	6
State Estimation	3
Output Feedback	4
Robustness	6

Learning Outcomes

Following the structure of the course topics, you should be able to perform the following after completing this class:

Dynamics and Feedback

Formulate simple dynamics (linear or nonlinear)
Define system states
Identify whether a system is linear or nonlinear
Perform linearization of a nonlinear system about an equilibrium state or trajectory
Write linear state description from dynamical equations

Dynamics of Linear Systems

Convert state space (SS) representations to transfer function (TF) representation
Convert TF representation to SS representation
Calculate canonical decompositions
Manipulate (calculate) transformations relating the realizations
Interconnect and perform analysis on an interconnected system
Determine whether a realization is minimal
Calculate the exponential of a matrix (expAt)
Understand and be able to apply the Cayley-Hamilton theorem
Perform controllability tests
Analyze system property effects on controllability
Perform obsesrvability tests
Identify controllable/observable subspaces
Perform a Kalman decomposition and reason about it!
Write a controllable realization
Write an observable realization
Write a controllable and observable realization
Understand and apply the concept of Lyapunov stability

Full State Feedback

Perform pole placement
Prove state feedback does not affect observability

State Estimation

Design an observer and place observer eigenvalues
Prove observer feedback does not affect controllability

Output Feedback

Write a reduced order observer

Robustness

Calculate TF for disturbance rejection
Analyze disturbance rejection
Perform optimal pole placement
Understand estimation with noise

General

Do simple proofs
Adequately apply course principles to reason about simple open problems