| 内容提要: |
In this paper, we study the problem of state feedback
stabilization of a linear time-invariant (LTI) discrete-time
multi-input system with imperfect input channels. Each input
channel is modeled in three different ways. First it is modeled
as an ideal transmission system together with an additive norm
bounded uncertainty, introducing a multiplicative uncertainty
to the plant. Then it is modeled as an ideal transmission system
together with a feedback norm bounded uncertainty, introducing
a relative uncertainty to the plant. Finally it is modeled as an
additive white Gaussian noise channel. For each of these models,
we properly define the capacity of each channel whose sum yields
the total capacity of all input channels. We aim at finding the
least total channel capacity for stabilization. Different from the
single-input case that is available in the literature and boils down
to a typical H or H optimal control problem, the multi-input
case involves allocation of the total capacity among the input
channels in addition to the design of the feedback controller. The
overall process of channel resource allocation and the controller
design can be considered as a case of channel-controller co-design
which gives rise to modified nonconvex optimization problems.
Surprisingly, the modified nonconvex optimization problems,
though appear more complicated, can be solved analytically. The
main results of this paper can be summarized into a universal
theorem: The state feedback stabilization can be accomplished
by the channel-controller co-design, if and only if the total input
channel capacity is greater than the topological entropy of the
open-loop system. |