**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