This paper gives some necessary and sufficient conditions for a linear decentralized control system with no information exchange between its control stations to be observable.
Consider a system with two control stations,
x(
k+1)=
Ax(k)+
B1u1(
k)+
B2u2(
k),
yi(
k)=
Cix(
k), (
i=1, 2,
k=0, 1, 2, …), where
ui is an
ri vector and
yi is an
mi vector. Let the set
Zi(
k) of data available to station
i at time
k be
Zi(
k)={
yi(0), …,
yi(
k),
ui(0), …,
ui(
k-1)}.
Then a necessary and sufficient condition for the system to be observable by station
i is that (i) rank
CiBj=rank
Bj, and (ii)
A33 is a nilpotent matrix, (
i=1,
j=2 or
i=2,
j=1), when the system and the measurement equations of the
i-th station are transformed into a canonical form, where
A11:
rj×
rj, and {
A22,
C22}; observable pair (in usual sense).
For the case where
mi=
rj, another necessary and sufficient condition is given, and it is also shown that a necessary condition for the system to be observable by station
i is that (i) {A, C
i} is an observable pair (in usual sense), (ii)
CiBj is non-singular, and (iii) {
A,
Bj} is a controllable pair.
抄録全体を表示