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Talk abstract:
Stabilization, Lyapunov-Like Functions, and the Effect of Disturbances
Eduardo Sontag, Rutgers University
This expository talk describes several recent results in the areas of
stability and stabilization of nonlinear control systems.
The first part will survey relationships between the existence of feedback
stabilizers and control-Lyapunov functions (cLf's).
The focus will be on correspondences between, respectively,
- stabilizability and continuous cLf's, and
- closed-loop robustness to "small" disturbances and smooth cLf's.
In particular, the issue of discontinuous feedback stabilization leads one to
a definition of "closed-loop behavior" which originates in the theory of
differential games. Techniques from nonsmooth analysis (viscosity-like)
are used in the construction of stabilizers.
Time permitting, the second part of the talk will shift into the effect of
"large" disturbances, and notions of stability that take into account external
perturbations. The concepts of input-to-state stability (ISS), as well as the
more recently introduced integral input-to-state stability (IISS), provide a
theoretical framework in which to analyze the issues that arise in this
context. The focus will be on dissipation (Lyapunov-like) characterizations
of these properties.
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