5.Consider a controllable and observable continuous time system described by

5.Consider a controllable and observable continuous time system described byddxx(t)=Ax(t)+Bu(t)y(t)=Cx(t)Find the optimal state feedback control law that minimizes the performance index:Ja=eaat((t)y()u(t)Ru(t)at,a>00where R is positive definite.Hint:Notice that Ja can be re-written by usingx(t)=eatx(t)u(t)=eatu(t)