Infinite zero structure of polynomial matrix and impulsive modes of polynomial matrix systems

In this paper, impulsive mode problem of polynomial matrix systems (PMSs) is investigated by analyzing the infinite zero structure of polynomial matrix. Some useful definitions and lemmas associated with linearization are introduced first, then a sufficient condition for PMSs having no impulsive modes is derived by using strong linearization approach. Based on dual polynomial matrix, the structure of infinite zeros for matrix pencil is analyzed and extended to general polynomial matrices. An algorithm is presented to compute the infinite zeros structure for arbitrary polynomial matrices. Finally, the numerical examples are given to illustrate the main results.