Stabilizing feedback for dynamical systems with bounded disturbances (Q1386961)

The authors study a regulation problem for completely observable, completely controllable linear systems with single input and bounded disturbances \[ \dot x= Ax+ bu+ w(t),\quad y= Hx. \] More precisely, given \(L> 0\), \(\varepsilon> 0\) and an open neighborhood \(G\) of the origin, it is required to find \(u= u(x)\) in such a way that 1) \(| u(x)|\leq L\), for \(x\in G\), 2) \(u\) asymptotically stabilizes the system when \(w= 0\), 3) for each \(x_0\in G\) there exists \(t^*\) such that \(| y(t)|<\varepsilon\) for \(t> t^*\). The problem is reduced to solving an associated optimization problem. The results are illustrated by a number of applicative examples.