An iteration method for exponential stability of linear time-varying singularly perturbed systems

An iteration method is proposed to investigate the exponential stability of linear time-varying singularly perturbed systems. By applying the variation-of-constants formula, an iterative process is introduced to approximate the solution of system under consideration. Then using the internal relations between iterative convergence and stability, a sufficient condition that ensures exponential stability for sufficiently small singular perturbation parameter is derived. Moreover, the stability bound of singular perturbation parameter can be obtained by calculating the spectral radius of certain parameter matrix. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.