Small gain theorems for large scale systems and construction of ISS Lyapunov functions
By Sergey N. Dashkovskiy, Björn S. Rüffer, Fabian R. Wirth. IEEE Conference on Decision and Control, 2009
398 citations recorded by the source corpus.
We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems.
Subfields: Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/cd80993bc19d274ff1fb0be07d8f2b5698a8d11e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Networks and Communications
In Control and Systems Engineering
- Andrii Mironchenko
- Hiroshi Ito
- Michael Kosmykov
- Lars Naujok
- Sergey N. Dashkovskiy
- Björn S. Rüffer
- Anders Rantzer
- David John Hill
Citations in the corpus
- Input‐to‐state exponents and related ISS for delayed discrete‐time systems with application to impulsive effects (2018, background): “FIGURE 1 Exponential input-to-state stability (IS-e−) of (18) with a = 0.”
- Separable Lyapunov functions for monotone systems: Constructions and limitations. (2015, background): “For this case it was shown in [25, 8] that under suitable conditions V (x) = maxi σ −1 i ( Vi(xi) ) is a Lyapunov function for the composite system (5), where the functions σi are appropriate scaling functions.”
- Monotone inequalities, dynamical systems, and paths in the positive orthant of Euclidean n-space (2010, neutral): “To this end note that the implication”
- Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods (2010, methodology): “However, if the small-gain condition holds, then we can construct non-exponential Lyapunov functions for the whole system as in [31], [18].”