Feedback Control of Nonstandard Singularly Perturbed Systems

This paper studies feedback control of linear time-invariant singularly perturbed systems of the form x = A
11
x + A
12
z + B
1
u ϵZ = A
21
x + A
22
z + B
2
u y = C
1
x + C
2
z + Eu. where A
22
may be singular. It is shown that, under stabilizability-detectability assumptions on the slow and fast models, the theory of feedback control of singularly perturbed systems can be extended to the case of singular A
22
. Both state and output feedback results are given.