E.g.Find a state spacedescription for the system describedbythefollowingdifferential equation3j+6j+12i+9y=6ü+3uSolution :For the system, n=3a, = 2,αz = 4,α, = 3,b = 0,b, = 0,b, = 2,b, =1[βo=bo= 0xi = y-βouβ =b -a,β=0x=j-βi-βuβ, =b, -αβ -α,β= 2X=-Bi-βu-βuβ = b, -a,β, -αzβ -a,β=1- 2×2 =-3
E.g. Find a state space description for the system described by the following differential equation 3 6 12 9 6 3 y y y y u u + + + = + Solution ： For the system, n=3 1 2 3 0 1 2 3 a a a b b b b = = = = = = = 2, 4, 3, 0, 0, 2, 1 0 0 1 1 1 0 2 2 1 1 2 0 3 3 1 2 2 1 3 0 0 0 2 1 2 2 3 b b a b a a b a a a = = = − = = − − = = − − − = − = − = − − − = − − = − x y u u u x y u u x y u 3 0 1 2 2 0 1 1 0
So, the state space description of system can be obtained asTβ001X=0X+β20uB3-a3-a2-ai0100001X+2u-2-3-3-4y=[10o]X+[β]u=[10 0]Xwhere X-[xx2x:]
So, the state space description of system can be obtained as T 1 2 3 X = x x x 1 2 3 2 1 3 0 1 0 0 0 1 0 1 0 0 0 0 1 2 3 4 2 3 u a a a u = + − − − = + − − − − X X X 0 1 0 0 1 0 0 y u = + = X X where