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In this paper we study the H∞ tracking problems with preview for a class of linear discrete-time Markovian jump systems. The systems are described by a class of switching systems with Markovian mode transition. The necessary and sufficient conditions for the solvability of the H∞ tracking problem are given by coupled Riccati difference equations with terminal conditions. Correspondingly feedforward compensators introducing future information are given by coupled difference equations with terminal conditions. In this paper we focus on the derivation method of noncausal compensator dynamics from the point of view of dynamics constraint. We derive the pair of coupled noncausal compensator dynamics and coupled Riccati difference equations by calculating the first variation of the performance index under the dynamics constraint.