P6.21 Consider the system described in state variable form by

* (1) = Ax(t) + Bu(t) y(t) = Cx (1) where 0 1 A: -k -k2 B = | | ], and C = [1 1 ], and where k = k2 and both k and k are real numbers. (a) Compute the state transition matrix (1, 0). (b) Compute the eigenvalues of the system matrix A. (c) Compute the roots of the characteristic polyno- mial. (d) Discuss the results of parts (a)-(c) in terms of stability of the system.