Abstract

The exact solutions of switching linear dynamical systems with arbitrary discontinuous forcing are investigated. The switching system consists of countable prescribed linear subsystems with specified external excitations. The traditional treatments are to smoothen the discontinuity between two subsystems in such a switching system. In this paper, a method is introduced to obtain an exact solution of such a switching system. Under periodic piecewise forcing and random forcing, the exact solutions and stochastic responses of switching systems are given to help one better understand random responses in stochastic dynamical systems. For periodic forcing, the periodic responses and stability of the switching system are presented.

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