Control System Design

Determine the feedback gain k that minimizes the performance index J = fo [ xt(t) x(t) + ut(t)u(t)] dt
for
where

x(t)_ 1°0 oTs(t) [°,] Li(t), ,(0)= Pol
u(0= — [ k k I x(t).
What is the value of ? Do not use the Riccati equation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample Solution