On stability of compound controlled systems (Q1902743)

Let \({\mathcal U}\) and \({\mathcal F}\) be classes of vector functions depending on the scalar \(t\) and let \(A: {\mathcal U}\to {\mathcal F}\). It is assumed that the motion \(x= \xi (t)\) is determined by the following compound system \(\dot x= X(t, x, u)\), \(Au=f\). Sufficient conditions for different types of stability of the motion \(x= \xi (t)\) are derived. The developed technique is applied to the problem of control and stabilization of angular motion of a rigid body with a fixed point.