EE6620 Assignment 1 (Sem A 2021/22)
Submission Instructions
1. Answer all questions.
2. Except for programs, answers must be hand-written. For program, give your program list
and copy the outputs of your program
3. Generate a pdf file for your answers and submit via Assignment in CANVAS. Deadline
for submission: 11:59pm 18-Sept-2021
4. You should make sure that the pdf file is clear enough for marking.
5. Late submission penalty: 25% deduction per day (Note: Late less than 24 hours is counted
as one day)
Q1. Consider a mapping function of input 𝑢(𝑡) and output 𝑦(𝑡) as below
𝑦(𝑡) = max(𝑢(𝑡), 𝑢(𝑡 − 1), 𝑢(𝑡 − 2))
Here, 𝑚𝑎𝑥(⋅) returns the largest value of its arguments.
Determine whether the mapping function is
(a) additive
(b) homogeneous
and prove your answers. [15 marks for each]
Q2. Consider the following circuit
Figure Q2. RLC system
(a) Derive the relationship of 𝑣𝐶2(𝑡) and 𝑖(𝑡) and give your answer as an ordinary differential
equation. [30 marks]
(b) Based on (a) and assuming that all the initial values are zero, determine the values of 𝑅, 𝐶1, 𝐶2
and 𝐿 such that the transfer function of the RLC system is
)54)(1()(
)(
2
2
2
sss
s
sI
sVC
[10 marks]
Q3. Consider a nonlinear system
�̇�1(𝑡) = 𝑥1(𝑡)𝑥2(𝑡) + 2𝑥1(𝑡)
�̇�2(𝑡) = 𝑥1(𝑡) − 𝑥2(𝑡) − 1
(a) Find all the equilibrium points of the nonlinear system. [10 marks]
(b) Design a MATLAB program for the system. Set the initial conditions 𝑥(0) close to the
equilibrium points (but not equal) and, plot 𝑥1(𝑡) against 𝑡 for each case. Show the results and
describe your observation. [20 marks]
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