1. LECTURE 39: APPLICATIONS OF STATE VARIABLES
Objectives:
Review of State Equations Example – Two-Car Motion Time-Domain Response Transfer Function Course Evaluations
Resources: WikiBooks: State Variables WC: State Variables
MS Equation 3.0 was used with settings of: 18, 12, 8, 18, 12.
Audio:
URL:

2. Discrete-Time Systems
The discrete-time equivalents of the state equations are:
The process is completely analogous to CT systems, with one exception: these equations are easy to implement and solve using difference equations 
For example, note that if v[n] = 0 for n ≥ 0,
and An is the state-transition matrix for the discrete-time case.
The output equation can be derived following the procedure for the CT case:
The impulse response is given by:
]i=k,

3. Solutions Using the z-Transform
Just as we solved the CT equations with the Laplace transform, we can solve the DT case with the z-transform:
Note that historically the CT state equations were solved numerically using a discrete-time approximation for the derivatives (see Section 11.6), and this provided a bridge between the CT and DT solutions.
Example:
]i=k,

4. State Variable Equations and Solutions – CT Systems
Recall our state equations for CT systems:
the time-domain solutions:
and the frequency domain solutions:
An equivalent formulation exists for discrete-time (DT) systems.
]i=k,

5. Example – Coupled Two-Car System

6. Example (Cont.)

7. Example (Cont.)

8. Example (Cont.)

9. Example (Cont.)

10. Example (Cont.)

11. Example (Cont.)

12. Example (Cont.)

13. Example (Cont.)

14. Summary Introduced the discrete-time versions of the state equations.
Reviewed an example in the textbook (Kamen and Heck) demonstrating the use of state variables on a real application.
Demonstrated how to solve this system in MATLAB.
The end…