Stability of networked systems with switching topologies
Karthik Gopalakrishnan, Hamsa Balakrishnan, Richard Jordan · 2016
The evolution of many networked systems, such as air transportation, can be modeled using a combination of the network topology and the resultant dynamics. In particular, time-varying networks can be represented by switching between candidate topologies. This paper models such systems as discrete-time, positive Markov Jump Linear Systems. Time-varying, periodic Markovian transition matrices and continuous state resets during discrete-mode transitions are also incorporated. Two notions of stability are considered: Mean Stability and Almost-Sure Stability, and appropriate conditions are derived for both of them. The analysis techniques are demonstrated using models determined from operational air traffic delay data. The results show that air traffic delay networks satisfy the proposed conditions for both mean stability and almost-sure stability, implying that delays tend to decay over time, even though several of the component discrete modes are unstable. Different nodes (airports) are also evaluated in terms of the persistence of delays and their susceptibility to network effects.