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IEEE TRANSACTIONS ON AUTOMATIC CONTROL, OCTOBER 1974and, with sensor trajectories sI = 1 -2t and s2 = 1t,Hence, by Theorem 1, the system is observable.5(4tt 2 + l)], det T = 0 on [0,1] and the system is not observable. constant matrices and Dl, > 8 2 2 > . . . > Bnn > 0, we obtain the following corollary.Corollary: A necessary and sufficient condition for observability is that every C; has rank (ni + l ) , i = l , . -. , n .