Decentralized blocking zeros. I. Decentralized strong stabilization problem

The authors consider the synthesis of decentralized stabilizing controllers with a minimum number of unstable poles for linear time-invariant finite-dimensional systems. The new concept of decentralized blocking zeros, which is an appropriate generalization of blocking zeros to multichannel systems, plays a crucial role. Decentralized blocking zeros are introduced and the decentralized strong stabilization problem (DSSP), which is the standard decentralized stabilization problem with stable local controllers, is considered. It is shown that DSSP has a solution just in the case where the multichannel system is free of unstable decentralized fixed modes and the parity interlacing property is satisfied between the real nonnegative poles and real nonnegative decentralized blocking zeros. The problem of synthesizing a decentralized stabilizing controller with a minimum number of unstable poles is a generalization of DSSP. This minimum number turns out to be the number of odd distributions of real nonnegative poles among the real nonnegative decentralized blocking zeros. It is also shown that the unstable poles of a decentralized stabilizing controller can nearly arbitrarily be distributed (spread) among the poles of the local controllers.