Stability and stabilization: discontinuities and the effect of disturbances

This expository paper deals with several questions related to stability and stabilization of nonlinear finite-dimensional continuous-time systems. The topics covered include a review of stability and asymptotic controllability, an introduction to the problem of stabilization and obstructions to continuous stabilization, the notion of control-Lyapunov functions, and a discussion of discontinuous feedback and methods of nonsmooth analysis. An emphasis is placed upon relatively new areas of research which concern stability with respect to noise, including the notion of insensitivity to small measurement and actuator errors as well as the more global notion of input-to-state stability.

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