No. of Pages: 2

API ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER M.TECH DEGREE EXAMINATION, APRIL/MAY 2018
Branch: ELECTRICAL & ELECTRONICS ENGINEERING

Stream(s): Control Systems, Guidance & Navigation Control

Course Code ಹ Name: 01EE6104 & NONLINEAR CONTROL SYSTEMS

Answer any two full questions from each part

Limit answers to the required points.

Max. Marks: 60 Duration: 3 hours
PARTA
1. a. State and explain Poincare Bendixon Criteria for the existence of limit cycles.
(4)
b. Whether the periodic orbits comply to the existence and un.iqueness theorem.
[f so explain the theorem. (5)
2. a. Define equilibrium point. List the classification of equilibrium points. (4)

b. For non-linear system having differential equation :

೫-೦ y +Y+y2 =o
Find all the singularities. (5)
3. Give an account of how Lipschitz condition simplified existence and uniqueness
theorem. (9)
PART 8

Construct a Lyapunov function for the following system usi_ng Variable
Gradient Method: = -3X2 —f(X1)

ಸಾ = - 22+1(% 1)

Non- linearity f = 8 (xo. Xl

(9)

೨, a. State and explain Circle Criteria