Answer Happy

Question 5 (10 marks) Consider the linear time-varying state-space equation = A(t)x, where A(t) is an nxn time-varying matrix that satisfies the condition Ace) ([^(-)ar) = ({4(r)ar) Ace) for all e 2 4020. ) = Find the state transition matrix (t, to) for this system. Hints: • For any matrix functions F(t) and G(t), the derivative of their product satisfies the property d (F(t)G(t)) = dF(t) G(t) + F(t) dG(t) dt dt dt • For an n x n time-varying matrix B(t), the matrix exponential function is defined as Bk(t) exp[B(t)] = k! k=0 =