An extension of the routh array for the asymptotic stability of a system of differential equations with complex coefficients

摘要

In this paper, we establish two necessary and sufficient conditions for the asymptotic stability of a system of differential equations with complex coefficients. These conditions are expressed in terms of the partial fraction and continued fraction expansions of a certain function related to the characteristic polynomial of the system. We then work out a systematic procedure for testing the asymptotic stability of an nxn complex system, and we show how our results generalize the well-known Routh criterion for the asymptotic stability of an nxn real system.