10.1. Consider the continuous-time matrix pair: A= [1 -3 01 0 - 2 0 and B= L2 -2 -1 [11] 1 0 LO 1 (1) Using the MATLAB function 'eig' verify that A is not stable (indicating that we cannot trivially conclude that the pair (A, B) is stabilizable). (ii) Form the controllability matrix L = [B AB APB] and use the MATLAB function 'orth' to verify that the range space of L, is not the full space and the pair (A, B) is not completely controllable (again indicating that we can- not trivially conclude that the pair (A, B) is stabilizable) (iii) Use Theorem 10.2 to show that the pair (A, B) is in fact stabilizable. (iv) Repeat part () with [1 07 B= 1 0 0 1 and use Theorem 10.2 to show that this new pair (A, B) is in not stabilizable. Theorem 10.2. The system i = Ax+Bu is stabilizable if and only if there exists Z >0 and a matrix Z such that (AZO-BZ)+(AZ - BZ)* 0 and a matrix Z such that (AZO-BZ)+(AZ - BZ)*