Intrinsic stability: stability of dynamical networks and switched systems with any type of time-delays
David Reber, Benjamin Z. Webb · Nonlinearity · 2020
Abstract In real-world networks, interactions between network elements are inherently time-delayed. These time-delays can both slow and destabilize the network, leading to poor performance. However, not all networks can be destabilized by time-delays. Previously, it has been shown that if a network is intrinsically stable, it maintains stability when constant time-delays are introduced. Here we show that intrinsically stable networks and a broad class of switched systems remain stable in the presence of any type of time-varying time-delays whether these delays are periodic, stochastic, or otherwise. We apply these results to a number of well-studied systems to demonstrate that intrinsic stability is both computationally inexpensive and improves on previous stability methods. Furthermore, we prove that the asymptotic state of an intrinsically stable switched system is independent of both the system’s initial conditions and the presence of time-varying time-delays. Thus, we justify ignoring the occurance of any type of time-delays when modeling intrinsically stable real-world systems for asymptotic analysis, and provide an efficient means of engineering delay-robust systems.