Linear feedback control of nonlinear systems with a dominating conservative quadratic term (Q1392702)

A class of quadratic dynamic (control) systems is considered. First, conditions which are sufficient to ensure that the dynamic system is point dissipative (i.e., which guarantee the existence of a bounded region in \(R^n\) for which every trajectory of the system eventually enters and remains in it) are given. These conditions are expressed in terms of relations between the quadratic and the linear part of the system (when the quadratic part is conservative). Next, these conditions are applied to the problem of the existence of a linear feedback control so that the closed-loop system has the origin as an asymptotically stable point or is point dissipative.