On the stabilization of some nonlinear control systems: Results, tools, and applications. (English) Zbl 0984.93067
Clarke, F. H. (ed.) et al., Nonlinear analysis, differential equations and control. Proceedings of the NATO Advanced Study Institute and séminaire de mathématiques supérieures, Montréal, Canada, July 27-August 7, 1998. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 528, 307-367 (1999).
This huge survey considers mainly the case of those nonlinear systems of the form
\[
\dot x= f(x,u),
\]
whose equilibrium at the origin may be stabilized by non-stationary feedback as
\[
u= u(x,t).
\]
Some usual feedback design tools such as control Lyapunov functions, damping, averaging, backstepping are presented. Applications to some nonlinear partial differential equations are given.
For the entire collection see [Zbl 0913.00037].
For the entire collection see [Zbl 0913.00037].
Reviewer: Vladimir Răsvan (Craiova)
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C10 | Nonlinear systems in control theory |
| 34C29 | Averaging method for ordinary differential equations |
| 93D30 | Lyapunov and storage functions |
