  In this paper, we study a class of stochastic Generalized Linear Switched
System (GLSS), which includes subclasses of jump-Markov, piecewide-linear and
Linear Parameter-Varying (LPV) systems. We prove that the output of such
systems can be decomposed into deterministic and stochastic components. Using
this decomposition, we show existence of state-space representation in
innovation form, and we provide sufficient conditions for such representations
to be minimal and unique up to isomorphism.
