- #1

- 3

- 0

## Homework Statement

Given the LTI system X =Ax+Bu where

A =[ 0 1 0 0 0 0; a1 0 0 a2 0 0;0 0 0 1 0 0;0 a3 0 0 0 0; 0 0 0 0 0 1;0 0 0 0 a4 0];

B = [0 0 0 ;b1 0 0 ; 0 0 0 ;0 b2 0 ;0 0 0 ;0 0 b2];

and the parameters a1; a2; a3; a4; b1; b2 are all nonzero. Determine whether the system is completely controllable. If not, find the controllable subspace of the state space.

## The Attempt at a Solution

I tried systematically but it seems to long so i try by matlab by the following code

syms a1 a2 a3 a4 b1 b2

A =[ 0 1 0 0 0 0; a1 0 0 a2 0 0;0 0 0 1 0 0;0 a3 0 0 0 0; 0 0 0 0 0 1;0 0 0 0 a4 0];

B = [0 0 0 ;b1 0 0 ; 0 0 0 ;0 b2 0 ;0 0 0 ;0 0 b2];

Co = ctrb(A,B)

Thanks in advanced