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Zbl 0832.93047
Sontag, Eduardo; Teel, Andrew
Changing supply functions in input/state stable systems. (English)
[J] IEEE Trans. Autom. Control 40, No.8, 1476-1478 (1995). ISSN 0018-9286

The authors consider the system $\dot x= f(x, u)$, $f: \bbfR^n\times \bbfR^m\to \bbfR^n$, locally Lipschitz with $f(0, 0)= 0$. The system is ISS if there exists a positive definite $V(x)$, $V(0)= 0$, radially bounded $\bbfR^n\to \bbfR$ (a storage function) and two functions (in $K_\infty$) $\alpha$ and $\gamma$ such that $\dot V= (\nabla V\cdot f)\le \gamma(|u|)- \alpha(|x|)$. A combination of the $\gamma$ and $\alpha$ functions characterizes the ``input to gain'' for the system. The authors prove some relations for positive definiteness of the storage function and the existence of $K_\infty$ functions assuring that dissipation estimates for some composite systems are available.
[V.Komkov (Roswell)]

MSC 2000:: *93D10 Popov-type stability of feedback systems
93C10 Nonlinear control systems
93A99 General systems theory

Keywords: input to state stability; supply functions; positive definiteness; storage function; dissipation estimates

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