Robust Stability of Networks of iISS Systems: Construction of Sum-Type Lyapunov Functions

Hiroshi Ito, Zhong-Ping Jiang, Sergey N. Dashkovskiy, Bjorn S. Ruffer
2013 IEEE Transactions on Automatic Control  
This paper gives a solution to the problem of verifying stability of networks consisting of integral input-tostate stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnections of two subsystems. For large-scale systems, stability criteria relying only on gain-type information that were previously developed address only input-to-state stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general
more » ... ructure, this paper shows how to construct Lyapunov functions of the network by means of a sum of nonlinearly rescaled individual Lyapunov functions of subsystems under an appropriate small-gain condition. Index Terms-Large-scale systems, Integral input-to-state stability, Nonlinear systems, Lyapunov functions, Robust stability criteria. PHOTO HERE Hiroshi Ito (S'92-M'96-SM'09) received the B.E. degree,
doi:10.1109/tac.2012.2231552 fatcat:e3ovlj2f4zboxmhnpo2xkieyca