Partial lagrange stability for time-varying linear systems

In this paper, we apply Wazewski inequality and Gronwall-Bellman inequality to study Lagrange stability of time varying linear systems with respect to partial and whole variables. We derive sufficient conditions for system partial stability, equi-stability and uniform stability in the Lagrange sense. As corollaries, we obtain easily verifiable stability criteria involving only the coefficients of the right-hand side and its eigenvalues.