Limitations and capabilities of feedback for controlling uncertain systems (Q2712235)

This note presents important results of the authors concerning robust global stabilization (rgs) of discrete-time systems with parametric uncertainties and random disturbances.NEWLINENEWLINENEWLINECases where rgs is impossible are based on the existence of solutions to a polynomial inequality. In many cases, if terms in the process contain nonlinearities of the type \(y^k\) with \(k>1\), then rgs cannot be achieved. A section points out that if the process is sublinear, a nonparametric stabilizing feedback can be devised. Some related open problems are indicated.NEWLINENEWLINENEWLINEThe results are based on the authors' paper [IEEE Trans. Autom. Control 44, No. 9, 1777-1782 (1999; Zbl 0958.93085)] and on a forthcoming publication.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].