1. Consider the linear system x = A(t)x, where A(t) - A(t+T). Define a constant matrix B via the equation esl' = (T, 0), and let P(t) = eBto(0, t). Show that (a) P(t + T) = P(t). (b) $ (t, T ) = P-1(t) el (t-T) B] P(T). (c) The origin of x = A(t)x is exponentially stable if B is Hurwitz (having all eigenvalues with negative real parts). Notice that P(t) and P-1(t) are continuous functions of t, hence, they are bounded for t E [0, T]. Since they are periodic, they are bounded V t > 0. Also, for B Hurwitz, |eBtil