For Objective 1

1.1  Manipulating  Z Transform,its inverse

1.2  Relating Complex Operations to Laplace and Z Transforms

1.3  Sampling of signals; effect of sampling to transfer functions;

1.4   reconstruction of continuous data from sampled ones

For Objective 2

2.1 Transient responses of LTI systems and transient parameters

2.2 Steady state error and its relation to system characteristics

2.3 System modeling in discrete time and in Z domain

For Objective 3

3.1  using PD,PI,PID controllers and tuning their parameters according to the design specs and stability characteristics.

3.2 using root locus and tuning parameters according to the transient parameters required in the specs and characteristics of relative stability.

For Objective 4

4.1  system characteristics represented by Bode Plots, Phase margin, gain margin

4.2 Design of lag compensators for required system relative stability and transients based on gain margin, phase margin

4.3 Design of lead compensators for required system relative stability and transients based on gain margin, phase margin

4.4 Design of lead lag compensators for required system relative stability and transients based on gain margin, phase margin

4.5 When to use lead ;when to use lag and what Lead lag provides.

For Objective 5

5.1 Modeling discrete systems in state space and analyzing  the model sensitivity to systems parameters

5.2 analyzing controllability and observability in different spaces: normalized systems and nondecoupled systems

For Objective 6

6.1 design with state feedback

6.2 estimate state by designing an observer

6.3 Use estimated state in pole placement: use the state feedback in conjunction with observer design