Summary: Handout ­ ELEC 302
I/O and I/S/O representation of SISO linear systems
I/O I/S/O
variables: (u, y) variables: (u, x, y)
q d
dt y(t) = p d
dt u(t), n = deg q deg p d
dtx(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t)
u(t), y(t) R x(t) Rn,
A B
C D
R(n+1)×(n+1)
Impulse response
q d
dt h(t) = p d
dt (t) h(t) = D(t) + CeAtB, t 0
H(s) = L(h(t)) = p(s)
q(s) H(s) = D + C(sI - A)-1B
Poles - characteristic roots - eigenfrequencies
i, q(i) = 0, i = 1, · · · , n det(iI - A) = 0

Source: Antoulas, Athanasios C. - Department of Electrical and Computer Engineering, Rice University

Collections: Engineering