... etMx 0 .ThusNetMx 0 =0 (t ≥ 0) .Let t = 0, to find Nx 0 = 0. Then differentiate this expression k times in t and let t =0, to discover as well thatNMkx 0 =0 for k =0, 1, 2, Hence (x 0 )T(Mk)TNT= ... NMnx 0 = 0. Likewise,Mn+1= M(−βn−1Mn−1−···−β 0 I)=−βn−1Mn−···−β 0 M;and so NMn+1x 0 = 0. Similarly, NMkx 0 = 0 for all k.Nowx(t)=X(t)x 0 = eMtx 0 =∞k =0 tkMkk!x 0 ;and ... hyperplane to C(t) through 0. This means that there exists b = 0 suchthat b ·x 0 ≤ 0 for all x 0 ∈C(t).Choose any x 0 ∈C(t). Thenx 0 = −t 0 X−1(s)Nα(s) dsfor some control α, and therefore0...