1 Introduction
Monday, May 8, 2017
4:30 PM
State Feedback
Consider the n-dimensional single-variable state equation
where we have assumed
In state feedback, the input
Each feedback gain
to simplify discussion.
is given by
is a
This is called
1.
2.
3.
ENSC

3 Linear Algebra (d)
June 2, 2014
10:30 AM
Functions of a square matrix
Polynomials of a square matrix
If
is block diagonal such as
Where
and
are square matrices of any order then
and
Consider the similarity transformation
or
. We have
A polynomial with 1

3 Linear Algebra (c)
Wednesday, May 28, 2014
9:30 AM
Diagonal Form and Jordan Form
A real or complex number is called an eigenvalue of the
Any nonzero vector
satisfying
real matrix
if
is called
Eigenvect.
In order to find the eigenvalues of ,
This is a ho

2 Mathematical Descriptions of Systems (b)
Monday, May 12, 2014
10:30 AM
Example 1 - RLC Circuit
Developing state-space equations for RLC circuits
1) Assign capacitor voltages and inductor currents as state variables
2) Use Kirchhoff's laws to express the

ENSC 483
Summer 2017
Assignment 2
Due Date:
You dont need to deliver this assignment (its not for marks), but I suggest you solve it
before 4:30 PM, Monday May 29th
1) Consider a system with input and output . Three experiments are performed on the system

ENSC 483
Summer 2017
Assignment 3
Due Date: Wednesday June 14th, 4:30 PM
1. Consider the following figure. What is the representation of the vector with respect to
the basis cfw_1 , 2 ? What is the representation of 1 with respect to cfw_2 , 2 ? In each c

4 State-Space Solutions and Realizations (a)
June 4, 2014
9:30 AM
General Solution of LTI State-Space Equations
The problem is to find the solution excited by
The solution hinges on the exponential function of we studied in the previous chapter. For
examp

3 Linear Algebra (b)
Wednesday, May 21, 2014
9:30 AM
Linear Algebraic Equations
Consider a system of
equations and
unknowns.
Or the equivalent matrix equation
The system
is solvable if
Example 1
Consider
In what condition
is solvable?
MSE483 Su 14 Page 1

1 Introduction
Monday, May 5, 2014
10:30 AM
State Feedback
Consider the n-dimensional single-variable state equation
where we have assumed
to simplify discussion.
b
+
1/s
A
In state feedback, the input
Each feedback gain
is given by
is a
This is called
1.

2 Mathematical Descriptions of Systems (a)
Wednesday, May 7, 2014
9:30 AM
Continuous-time signal
Discrete-time signal
SISO
Properties of Systems
Memoryless
A system is called memoryless if
Causal or nonanticipatory
A system is called causal if
Practice:
A

https:/www.khanacademy.org/math/linear-algebra
3 Linear Algebra (a)
Wednesday, May 14, 2014
9:30 AM
The vector
is called the
The set of vectors
is said to be
if there exists real numbers
, not all zero, such that
If the only set of for which the above equ

4 State-Space Solutions and Realizations (c)
June 11, 2014
9:30 AM
Solution of Linear Time-Varying Systems
The material in this note is a generalization of previous discussions and it is valid for both
Fundamental Matrix
is called the fundamental matrix o

Assignment 5 Solution
Wednesday, July 9, 2014
8:48 AM
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4 State-Space Solutions and Realizations (b)
June 9, 2014
10:30 AM
Equivalent State-Space Equations
Example
Consider the following circuit. It consists of one inductor, one capacitor, one resistor, and one voltage
source.
First we select the inductor curr

Assignment 2 Solution
May 21, 2014
9:11 AM
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Assignment 5 Solution
Monday, July 17, 2017
8:48 AM
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6 Controllability and Observability (d)
Monday, June 30, 2014
10:30 AM
Kalman Decomposition
Consider
Let
, where
With
properties of
is a nonsingular matrix. Then the state equation
,
and
is equivalent to the previous equation. All
, including stability, c