Fall 2001 16.31122 Definition: A state o*+0 is said to be uncontrollable if the forced state response a(t)is orthogonal to x*vt>0 and all input functions You cannot get there from here This is equivalent to saying that a* is an uncontrollable state if 2 Bu(t-T2)di 2B(t-2)d2=0 Since this identity must hold for all input functions u(t-r2), this can only be true if B≡0t>0Fall 2001 16.31 12—2 • Definition: A state x? 6= 0 is said to be uncontrollable if the forced state response x(t) is orthogonal to x? ∀ t > 0 and all input functions. — “You cannot get there from here” • This is equivalent to saying that x? is an uncontrollable state if (x? ) T Z t 0 eAτ2Bu(t − τ2)dτ2 = Z t 0 (x? ) T eAτ2Bu(t − τ2)dτ2 = 0 • Since this identity must hold for all input functions u(t − τ2), this can only be true if (x? ) T eAtB ≡ 0 ∀ t ≥ 0