A Topological Approach to the Stability of Time-Varying and Nonlinear Networks

摘要

New techniques are presented which provide stability information for time-varying and nonlinear networks by inspection of the topology and the element values of the network. The derivation of the new techniques is based on Liapunov's second method for time-varying networks, his first method for nonlinear networks and network topology. More specifically, Liapunov's stability theorems of linear time-varying RLC networks are formulated in terms of the tree or chord-set products of the subnetorks derived from the state-space representation of the general networks. The local stability theorems of nonlinear time-invariant RC and RL networks are formulated in terms of the tree or chord-set products of subnetworks. Four examples are given to illustrate the above theorems. (Author)