Abstract by David Reber
Exponential Stability of Intrinsically Stable Dynamical Networks with Time-Varying Time-Delays
Dynamic processes on real-world networks are time-delayed due to finite processing speeds, the need to transmit data over distances, etc. These time-delays often destabilize the network's dynamics, but are difficult to analyze because they increase the dimension of the network. Consequently, the typical Lyapunov, LMI, and related means of analysis become prohibitively difficult, especially when these delays vary in time (i.e. stochastic, periodic, etc).
This talk presents recent results outlining an alternative means of analyzing these networks, by focusing analysis on the Lipschitz matrix of the low-dimensional undelayed network. Furthermore, the tools of this analysis can be applied to nonlinear switched systems of arbitrary dimension with uncountably many transition functions, given the transition functions are row-independant.
The key criteria, intrisic stability, is computationally efficient to verify by use of the power method. Multiple applications from control theory and neural networks will be presented.