Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
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

Highlights
Master Server