Abstract
While nonlinear scalings of Lyapunov functions are also Lyapunov functions, we provide examples that the same statement does not necessarily hold for Input-to-State Stable (ISS) Lyapunov functions or for integral ISS (iISS) Lyapunov functions. We provide sufficient conditions under which a nonlinear scaling of an ISS or iISS Lyapunov function is also an ISS or iISS Lyapunov function. We also introduce a generalization of the iISS Lyapunov function, which we term a dissipative iISS-Lyapunov function, that allows for a larger class of nonlinear scalings so that nonlinear scalings of dissipative iISS-Lyapunov functions are again dissipative iISS-Lyapunov functions.
Original language | English |
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Article number | 7163325 |
Pages (from-to) | 1087-1092 |
Number of pages | 6 |
Journal | IEEE Transactions on Automatic Control |
Volume | 61 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Apr 2016 |
Externally published | Yes |