We study the behaviour of dynamic power control algorithm and derive new sufficient conditions for the dynamic to be convergent. The convergence condition is based on the properties of diagonally dominant matrices and an additional condition required for the real parts of their eigenvalues to be negative. The essential condition for the power dynamic to be stable is expressed in terms of relationships between channel links, interference links and the required QoS on the channel links. We discuss the connection to previous works on convergent power control and present results from some numerical investigations