In this work, we study the pth moment input-to-state stability (ISS) property for discrete-time nonlinear Markovian switching systems. This property has been studied for discrete-time nonlinear switching systems in the current literature. In this paper, we present an ISS analysis for the Markovian switching case. Particularly, we introduce the definitions of pth moment ISS and exponential pth moment ISS for this class of systems, and we provide sufficient Lyapunov conditions, guaranteeing this property. We also show with an example that our conditions are essential for the analysis of Wireless Control Networks (WCNs), where the communication channel, used to convey information between network components, may suffer from packet-losses.
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