Exercise 6.1 Let X(t), Y(t) be nxn matrices satisfying the linear differential equation “) = Ht) (*) = with the boundary

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Exercise 6.1 Let X(t), Y(t) be nxn matrices satisfying the linear differential equation “) = Ht) (*) = with the boundary condition X(t1) = 1, Y(t1) = -2M, where H(t) is defined in (6.7). Check that the matrix P(t) y (1)X-1() (6.15) satisfies the RDE (6.14) and the boundary condition (6.11).

(3) = ( = Alt) {B(t)R-'(t)BT (t) 2Q(t) - AT (+) ***) (*) =: : H(t) (6.7)

P(t) = = P(t)A(t) A7 (t)P(t) Q(t) | P(t)B(t)R-1(t)BF(t)P(t) AT (BRt (6.14)

P(ti) = M. (6.11)