Fall 2001 16.318-3 ● Consider case2 y=Gs=+a182+028+0a3D(s 618+b2s+b3 yy u 0 u where y/v=Ns) and v/u=1/D(s) Then the representation of o/=1/D(s) is the same as case 1 a10+a20+a use the state vector U to get A C+ Bu where a1-a2-a3 100andB2=0 010 Then consider y/v=N(s), which implies that b1i+620+b30 [b1 b2 b3 U C2x+[0Fall 2001 16.31 8–3 • Consider case 2 y u = G(s) = b1s2 + b2s + b3 s3 + a1s2 + a2s + a3 = N(s) D(s) • Let y u = y v · v u where y/v = N(s) and v/u = 1/D(s) • Then the representation of v/u = 1/D(s) is the same as case 1 v(3) + a1v¨ + a2v˙ + a3v = u use the state vector x =   v¨ v˙ v   to get x˙ = A2x + B2u where A2 =   −a1 −a2 −a3 100 010   and B2 =   1 0 0   • Then consider y/v = N(s), which implies that y = b1v¨ + b2v˙ + b3v =  b1 b2 b3    v¨ v˙ v   = C2x + [0]u