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This paper proposes a time-varying matrix solution to the Brockettstabilization problem. The key matrix condition shows that if the system matrixproduct $CB$ is a Hurwitz H-matrix, then there exists a time-varying diagonalgain matrix $K(t)$ such that the closed-loop minimum-phase linear system withdecentralized output feedback is exponentially convergent. The proposedsolution involves several analysis tools such as diagonal stabilizationproperties of special matrices, stability conditions of diagonal-dominantlinear systems, and solution bounds of linear time-varying integro-differentialsystems. A review of other solutions to the general Brockett stabilizationproblem (for a general unstructured time-varying gain matrix $K(t)$) and acomparison study are also provided.

A time-varying matrix solution to the Brockett decentralized stabilization problem