The necessary and sufficient conditions of partial stability for linear dynamical systems (Q1813330)

The authors present a series of theorems on necessary and sufficient conditions for stability, attractability and boundedness with respect to a part of the variables, for time-varying linear systems (1) \(dx/dt=A(t)x\), \(x\in\mathbb{R}^ n\). The conditions are formulated in terms of the intercept matrix \(K_ m(t,t_ 0)=E_ mK(t,t_ 0)\) where \(K(t,t_ 0)\) is the Cauchy matrix of system (1), and \(E_ m\) denotes the \(n\times n\) matrix \(E_ m=\left({I_ m\atop0}{0\atop0}\right)\), \(1 \leq m < n\).