Fall 2007
線性系統
Linear Systems
Chapter 06
Controllability & Observability
Feng-Li Lian
NTU-EE
Sep07 – Jan08
Materials used in these lecture notes are adopted from
“Linear System Theory & Design,” 3rd. Ed., by C.-T. Chen (1999)
NTUEE-LS6-CtrbObsv-2
Feng-Li Lian © 2007
Outline
Introduction
Controllability (6.2)
Observability (6.3)
Canonical Decomposition (6.4)
Conditions in Jordan-Form Equations (6.5)
Discrete-Time State Equations (6.6)
Controllability after Sampling (6.7)
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Introduction (6.1)
¨
Controllability
and
observability
reveal
the
internal structure
of the system (
model
)
1
input
:
u
2
states
:
x
1
,
x
2
1
output
:
y
The state
x
2
is
NOT
“
controllable
” by the input
u
The state
x
1
is
NOT
“
observable
” at the output
y
=
−
x
2
+2
u
NTUEE-LS6-CtrbObsv-4
Feng-Li Lian © 2007
Controllability (6.2)