Control of decentralized systems with distributed controller complexity

An approach is presented which allows design of stabilizing decentralized controllers for linear systems with two scalar channels, such that each local controller is endowed with some dynamics while the sum of the orders is kept smaller than the system order. It is shown that for almost all
n
th-order systems with two scalar channels the local controllers can be chosen such that their orders δ
1
and δ
2
satisfy
\delta_{1} +\delta_{2}\leq n - 2
, max
{\delta_{1}, \delta_{2}} \leq max {(n - 1)/2, n -1 - (\mu_{0}/2)}
, whereμ
0
is the number of stable zeros of the cross Coupling transfer functions in the system. The approach is to design one of the local controllers such that the McMillan degree of the resulting one-channel system is reduced. Then the other local controller only has to deal with a model of reduced dimension and can thus be chosen of lower order.