Direct derivation method of noncausal compensators for linear continuous-time systems with impulsive effects

In this paper we study the H_∞ tracking problems with preview for a class of linear continuous-time systems with impulsive effects. The systems include linear continuous-time systems, linear discrete-time systems and linear systems with the input realized through a zero-order hold. The necessary and sufficient conditions for the solvability of the H_∞ tracking problem are given by Riccati differential equations with impulsive effects and terminal conditions. Correspondingly feedforward compensator introducing future information is given by linear differential equation with impulsive parts and 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 noncausal compensator dynamics and impulsive Riccati equations by calculating the first variation of the performance index under the dynamics constraint.