EEC 510: Linear Systems
9/7/2016
Lecture 3: State Equation Modeling (continued)
Relationship between transfer function and state equations
1. How to obtain transfer function from state equations?
x Ax Bu
State Equations:
y Cx
Laplace transform of State Eq

EEC 510: Linear Systems
9/21/2015
Lecture 7: Linear vector and space (continued)
1. Dimension and basis
Dimension: The maximum number of linearly independent vectors in a linear space (X, F)
is called the dimension of the space.
- In two dimensional real

EEC 510: Linear Systems
9/2/2015
Lecture 4: State Equation Modeling (continued)
Relationship between transfer function and state equations
1. How to obtain transfer function from state equations?
&
x = Ax + Bu
State Equations:
y = Cx
Laplace transform of

EEC 510: Linear Systems
9/14/2015
Lecture 6: Linear Vector and Space
1. Vectors
Vectors are interpreted as a magnitude and direction. (Defined physically)
- They are often restricted to two or three dimensions of physical space.
- They often have physical

EEC510: Linear Systems
8/26/2015
Lecture 2: Modeling of Physical Systems and
Introduction to State Equations
1. Modeling of physical systems
Clearly understand the purpose of this system
Determine the energy/power transfer characteristics of the system

EEC 510: Linear Systems
8/31/2015
Lecture 3: State Equation Modeling
1. Examples of state equation modeling.
Example 1: A mechanical system is shown as below. We take external force F as input and
displacements x1 and x2 as outputs. Please derive state eq

EEC 510: Homework 2
Due on Sept. 28, 2016
This homework is classified into two separate assignments. One is written assignment,
the other is Matlab assignment. For written assignment, you have to solve every problem
using hand calculation. For Matlab assi

EEC 510: Homework 1
Fall, 2016
Due on Sep. 14, 2016
You are encouraged to discuss with others to work out the homework problems. However, you
have to turn in your own work. Identical homework will receive a grade of zero. The problems
should be in order a

EEC 510: Linear Systems
9/26/2016
Lecture 6: Linear Space, Linear Operator, and
Simultaneous Equations
1. Dimension and basis
Dimension: The maximum number of linearly independent vectors in a linear space (X, F)
is called the dimension of the space.
- I

EEC510: Linear Systems
8/31/2016
Lecture 2: Introduction to State Equations
1. Introduction to state equations
Definition
- A collection of first-order differential equations
- Representing the same information as the original high-order differential equ

EEC 510: Linear Systems
9/12/2016
Lecture 4: State Equation Modeling (Continuous)
1. How to obtain state equations from transfer functions
Parallel-realization form
Example1:
TF ( s )
Y ( s)
4s 2 6s 5
3
U ( s ) s 7 s 2 14 s 8
4s 2 6s 5
( s 1)( s 2)( s

EEC 510: Linear Systems
9/14/2016
Lecture 5: Linear Vector and Space
1. Vectors
Vectors are interpreted as a magnitude and direction. (Defined physically)
- They are often restricted to two or three dimensions of physical space.
- They often have physical

EEC510: Linear Systems
8/29/2016
EEC 510 Linear Systems
Lecture 1: Introduction to Linear Systems
1. Frequency-domain and time-domain
Linear systems can be mathematically described in one of two domains: frequency
domain and time domain.
Frequency-domain

EEC 510: Linear Systems
9/9/2015
Lecture 5: State Equation Modeling and Linearization of
Nonlinear Systems
1. How to obtain state equations from transfer functions
Parallel-realization form
Example1:
TF ( s ) =
Y (s)
4s 2 + 6s + 5
= 3
U ( s ) s + 7 s 2 +