New estimation of solutions and partial Lagrange stability for a class of nonlinear time-varying systems

This paper gives a new estimation of solutions for a class of nonlinear time-varying systems via non-quadratic form Lyapunov function. Different from the Wazewski inequality, the method presented in the paper can avoid the difficult of computing eigenvalues of time-varying matrix. In addition, a new and easily verifiable algebraic criterion is obtained for the uniform Lagrange stability with respect to partial variables by applying the new estimation and some inequalities. Finally, one numerical example is given to show the effectiveness of the method.