b. Consider a non-linear system governed by the equation :

2)(2 291 +31 -- = 21
و - = 2

A candidate for Lyapunov function 15 V= Pli X1 2 + Pu X2 2 ; Pil < 0 and 1322 <0
which is a positive definite function. Check the stability for the system. Sketch

the region of stability.
(5)

a. Find the sector [0, k] for which the given transfer function is absolutely stable using
Popov Criteria.

1

G ‏ع‎ வகைகளாக

(5) (s+2)(s+3) (6)
b. Write short notes on Kalman's Conjecture. (3)
PART C

Find out a control law for the system :
= 2 sin 2
> -- -)(1 2 + ५
using feedback linearization control technique after suitable applying suitable
transformation. (12)
a. Explain stabilization via linearization. (3)

b. Apply back stepping to design a state feedback control law to globally stabilize
the origin.

=X2
=sin ப
(9)
a. Write notes on Integral control via linearization (6)

b. Write notes on Gain scheduling. (6)