A Time-Varying Matrix Solution to the Brockett Decentralized Stabilization Problem

This paper proposes a time-varying matrix solution to the Brockett stabilization problem. The key matrix condition shows that if the system matrix product CB is a Hurwitz H-matrix, then there exists a time-varying diagonal gain matrix K(t) such that the MIMO minimum-phase linear system with decentralized output feedback is exponentially convergent. The proposed solution involves several analysis tools such as diagonal stabilization properties of special matrices, stability conditions of diagonal-dominant linear systems, and solution bounds of linear time-varying integro-differential systems. A review of other solutions to the general Brockett stabilization problem (for a general unstructured time-varying gain matrix K(t)) and a comparison study are also provided.