Feedback Design for Robust Global Stability

Abstract

The purpose of this Chapter is to describe some important tools for the design of feedback laws which globally asymptotically stabilize a nonlinear system in the presence of parameter uncertainties. We consider the case in which the mathematical model of the system to be controlled depends on a vector μ ∈ ℝ^p of parameters, which are assumed to be constant, but whose actual values are unknown to the designer. The vector µ of unknown parameters could be any vector in some a priori given set $\mathcal{P}$, and the goal of the design is to find a feedback law (obviously independent of μ) which globally asymptotically stabilizes the system for each value of $\mu \in \mathcal{P}$. A problem of this type is usually referred to as a problem of robust stabilization.