ENSC 483
Spring 2014
Name:
Quiz 4
Consider a system with transfer function
( )
and an input whose Laplace transform equals
( )
(
)
a) Is the system asymptotically stable? (Choose Yes No Maybe) Why?
b) Is the system stable in the sense of Lyapunov? (Choose

ENSC 483
Spring 2014
Assignment 1
Due Date:
Saturday Jan 11, 11:59 PM
Edit your profile in Canvas and upload your photo! Pay attention that the photo should be clear
and identifiable!

Quiz 1 Solution
Wednesday, January 22, 2014
1:56 PM
Find a state-space representation of the circuit shown in the following figure. Find also its transfer function.
ENSC483 Sp14 Page 1
ENSC483 Sp14 Page 2

ENSC 483
Spring 2014
Quiz 2
Name:
1) What are the characteristic polynomial and minimal polynomial of the following matrix?
(1.5 marks)
[
]
( )
( )
2) Find a Jordan-form or diagonal-form representation ( and ) of the following matrix:
[
]
(3.5 marks)

Quiz 2 Solution
Wednesday, February 5, 2014
3:15 PM
You can see a more detailed solution in these two following links:
-Eigenvalue part
-Eigenvector part
ENSC483 Sp14 Page 1

ENSC 483
Spring 2014
Assignment 6
Due Date: Monday March 31st, 8:30 AM
1. Find a realization for the proper rational matrix:
(
( )
)(
[
)
]
2. Find a realization for each column of ( ) in problem 1 and then combine them, as
explained in class, to obtain a

ENSC 483
Spring 2014
Assignment 7
Due Date: Wednesday April 2nd , 8:30 AM
1. Is the network shown in the following Figure BIBO stable? If not, find a bounded input
that will excite an unbounded output. Why did you choose this specific input?
2. Is a syste

8 State Feedback and State Estimators (a)
Wednesday, July 16, 2014
9:30 AM
State Feedback
Consider the n-dimensional single-variable state equation
d
b
+
1/s
c
A
In state feedback, the input
Each feedback gain
is given by
is a
This is called
The obtained

4 State-Space Solutions and Realizations (e)
July 7, 2014
10:30 AM
Realization of SIMO systems
The vector on the right
is strictly proper. Let the following monic polynomial
be the least common denominator of all entries of
Then we have
The controllable r

5 Stability (a)
Wednesday, March 19, 2014
8:30 AM
Systems are designed to perform some tasks or to process signals. If a system is not stable, the system
may burn out, disintegrate, or saturate when a signal, no matter how small, is applied. Therefore, an

ENSC 483
Spring 2014
Assignment 8 (Optional)
I will post the solutions on Wednesday April 9th. I will also solve it in class on that day.
1. Given
( )
] ( )
[
( )
[
[ ] ( )
] ( )
Find the state feedback gain so that the state feedback system has
eigenvalu

Quiz 4 Solution
Wednesday, April 2, 2014
6:05 PM
ENSC 483
Spring 2014
Name:
Quiz 4
Consider a system with transfer function
and an input whose Laplace transform equals
a) Is the system asymptotically stable? (Choose Yes No Maybe) Why?
b) Is the system sta

8 State Feedback and State Estimators (d)
Monday, July 28, 2014
10:30 AM
State Estimator (State Observer)
Previously, we introduced state feedback under the implicit assumption that all state variables are
available for feedback.
This assumption may not h

ENSC 483
Spring 2014
Assignment 5
Due Date: Wednesday March 19th, 8:30 AM
1. Is the following state-space equation controllable? Observable? (Find controllability and
observability matrices)
( )
] ( )
[
( )
[
[ ] ( )
] ( )
2. Is the following state-space

ENSC 483
Spring 2014
Assignment 4
Due Date: Monday February 24th, 8:30 AM
1. An oscillation can be generated by
( )
[
] ( )
Show that the solution is
( )
[
] ( )
2. Use the following two methods to find the unit step response of
( )
] ( )
[
( )
where ( )

ENSC 483
Spring 2014
Assignment 3
Due Date: Monday February 3rd , 8:30 AM
1. Consider the following figure. What is the representation of the vector
the basis
? What is the representation of with respect to
redraw the figure and explain your answer.
with

8 State Feedback and State Estimators (b)
Monday, July 21, 2014
10:30 AM
Stabilizability
If a state equation is controllable, all eigenvalues can be arbitrarily assigned by introducing state
feedback. We now discuss the case when the state equation is not

8 State Feedback and State Estimators (c)
Wednesday, July 23, 2014
9:30 AM
State Feedback - MIMO Case
Definition of a Cyclic Matric
A matrix is called cyclic if
In other words, a matrix is called cyclic if its
Theorem
If the n-dimensional p-input pair (A,

ENSC 483
Spring 2014
Assignment 2
Due Date:
You dont need to deliver this assignment, but I suggest you solve it before 8 AM, Monday
Jan 20th
1) Consider a system with input and output . Three experiments are performed on the system
using the input ( ) (

4 State-Space Solutions and Realizations (d)
July 2, 2014
9:30 AM
Realization of SISO systems
Every SISO linear time-invariant (LTI) system can be described by the input-output description
And, if the system is lumped as well, by the state-space equation

5 Stability (b)
Wednesday, July 9, 2014
9:30 AM
Internal Stability
The BIBO stability is defined for zero-state responses. We now discuss stability of zero-input
responses.
If
is identically zero for all
then the state-space equation reduces to
For zero-i