Eigenvalues and Eigenvectors
Definition. Let A be a linear operator from C" to C.
A scalar FL is called an eigenvalue of A if 3 a nonzero
x E C, such that AX = XX <=> (AI-Ah: = 0.
(M - A)X = 0 has a non-zero sol. iff A0.) = |M - A| = 0
w Characteristic
Some properties for eAl
From the denition,
on kk 22 33
emzzAt =I+At+At +At
H, k! 2 3!
+.
The following can be veried
At At 1
e =(e ) ;
Caution: eA+B usually does not equal to eAeB.
We only have eA+B=eAeB when AB=BA More properties:
eL?
dt
M m Ak
Inverted Pendulum
.
For this example, let's assume the following quantities:
(M)
mass of the cart
0.5 kg
(m)
mass of the pendulum
0.2 kg
(b)
coefficient of friction for cart
0.1 N/m/sec
(l)
length to pendulum center of mass
0.3 m
(I)
mass moment of inerti
Different representations of vector x
X=[1 3] q1= [3 1] q2= [2 2]
Find the representation of X with respect to the basis
cfw_q1 q2 and cfw_q2, i2.
Modeling in the Time Domain
Introduction
The basic questions that will be addressed in state-space
approach
EE 510 Linear Systems
Instructor:
Office:
Phone:
Email:
Office Hours:
Dr. Shuo Pang
LB 360
226-7038
[email protected]
Mon 1:00-3:00pm
Tue 2:00-3:30pm
Wed 1:00-2:00pm
others by appointment
EE 510 Grading
Two exams will be given during the term.
Points w