Input-to-state stability of interconnected hybrid systems
Sergey Dashkovskiy, Michael Kosmykov
TL;DR
This paper investigates the stability of interconnected hybrid systems, demonstrating that the input-to-state stability (ISS) property is preserved under certain conditions and providing a method to construct ISS-Lyapunov functions.
Contribution
The paper establishes ISS of interconnected hybrid systems under small gain conditions and offers an explicit construction of non-smooth ISS-Lyapunov functions.
Findings
ISS is maintained in interconnected hybrid systems if the small gain condition holds.
An explicit method for constructing non-smooth ISS-Lyapunov functions is provided.
The results apply to systems with arbitrary interconnection topologies.
Abstract
We consider the interconnections of arbitrary topology of a finite number of ISS hybrid systems and study whether the ISS property is maintained for the overall system. We show that if the small gain condition is satisfied, then the whole network is ISS and show how a non-smooth ISS-Lyapunov function can be explicitly constructed in this case.
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Taxonomy
TopicsStability and Control of Uncertain Systems · Neural Networks Stability and Synchronization · Control and Stability of Dynamical Systems