Some remarks on noncausal systems design for linear continuous-time Markovian jump systems from the point of view of computational algorithms

In order to design tracking systems (control or state estimation) for a class of systems with rapid or abrupt changes, it is effective in improving tracking performance to consider future information of reference signals or observations, i.e., noncausal information. In this paper we study H_∞ tracking control problems with preview and H_∞ smoothig problems for a class of linear continuous-time Markovian jump systems by unified game theoretic approach. We also give some remarks on noncausal systems design for such systems from the point of view of computational algorithms on actual design of large-scale highly functional systems. The necessary and sufficient conditions for the solvability of the H_∞ tracking control problems by state feedback and H_∞ smoothing problems are given by coupled Riccati differential equations with terminal conditions and initial conditions respectively. Correspondingly noncausal compensators introducing future information are given by coupled differential equations with terminal conditions, while causal controllers or estimators are uncoupled.