General solution and stability

Abstract

Just as in the case of time-invariant systems, the general solution of a time-variant system is determined by its fundamental matrix. Although for general time-variant systems the fundamental matrix cannot be explicitly calculated, for periodically time-variant systems the precise structure of the fundamental matrix is given by the Floquet theory. The criteria for stability and boundedness can also be found by means of the Floquet theory. This section concludes with an analysis of the particular properties of mechanical systems.