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We consider arbitrarily many interconnected integral Input-to-State Stable (iISS) systems in an arbitrary interconnection topology and provide an (i)ISS comparison principle for networks. We show that global asymptotic stability of the origin (GAS) of a lower-dimensional system termed the comparison system, which is based on the individual dissipative Lyapunov iISS inequalities, together with a scaling...
In the framework of the ISS Lyapunov formulation a small gain theorem has recently been proved which allows the explicit construction of Lyapunov functions for interconnected systems. In this note we recall the definitions of ISS Lyapunov functions and the corresponding general small gain theorems. These are then exemplarily used to prove input-to-state stability of and to construct ISS Lyapunov functions...
We consider networks of locally input-to-state stable (LISS) systems. Under a small gain condition the entire network is again LISS. An efficient numerical test to check the small gain condition is presented in this paper. An example from applications serves as a demonstration for quantitative results.
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