Mathematics – Optimization and Control
Scientific paper
1999-02-03
Mathematics
Optimization and Control
48 pages See http://www.math.rutgers.edu/~sontag/ for many related papers. See also the book "Mathematical Control Theory: Det
Scientific paper
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
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