Abstract
In this paper we study the H∞ tracking problems with preview by state feedback for a class of linear continuous-time systems with impulsive effects and stochastic uncertainties on the finite time interval. The systems include linear stochastic continuous-time systems, linear stochastic discrete-time systems and linear systems with stochastic uncertainties and an input realized through a zero-order hold. The author has already presented the necessary and sufficient conditions for the solvability of these H∞ tracking problems and given the control strategies for them respectively ([11]). The necessary and sufficient conditions for the solvability of the H∞ tracking problem are given by Riccati differential equations with impulsive parts and terminal conditions. Correspondingly feedforward compensator introducing future information is given by linear differential equation with impulsive parts and terminal conditions. It is a very important point in this theory. However it has not been yet investigated how the preview feedforward compensator with impulsive parts and effects of stochastic uncertainties of the systems is derived in detail. In this paper we focus on the direct 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 stochastic first variation of the performance index under the dynamics constraint.
