Stability and stabilization: Discontinuities and the effect of disturbances
Abstract
Description
In this expository paper, which covers material presented at the NATO Advanced Study Institute "Nonlinear Analysis, Differential Equations, and Control" (Montreal, Jul/Aug 1998), we deal with several questions related to stability and stabilization of nonlinear finite-dimensional continuous-time systems.
We review the basic problem of feedback stabilization, placing an emphasis upon relatively new areas of research which concern stability with respect to "noise" (such as errors introduced by actuators or sensors).
The table of contents is as follows:
Review of Stability and Asymptotic Controllability
The Problem of Stabilization
Obstructions to Continuous Stabilization
Control-Lyapunov Functions and Artstein's Theorem
Discontinuous Feedback
Nonsmooth CLF's
Insensitivity to Small Measurement and Actuator Errors
Effect of Large Disturbances: Input-to-State Stability
Comments on Notions Related to ISS
48 pages See http://www.math.rutgers.edu/~sontag/ for many related papers. See also the book "Mathematical Control Theory: Deterministic Finite Dimensional Systems" (http://www.math.rutgers.edu/~sontag/mct.html) for background material
48 pages See http://www.math.rutgers.edu/~sontag/ for many related papers. See also the book "Mathematical Control Theory: Deterministic Finite Dimensional Systems" (http://www.math.rutgers.edu/~sontag/mct.html) for background material