Game-theoretic estimation for continuous-time systems with single time-delay in the observations

In this paper, we will propose a novel approach to study the game-theoretic estimation problems for linear continuous-time systems with single output delays, in which the non-casual game-theoretic estimators satisfy the saddle-point conditions of a two-player zero-sum differential game. First, we will construct new delay-free measurements which are close relationships with original measurements. Then, based on the new measurements, the non-casual game-theoretic estimators satisfying the saddle point inequality can be designed by applying the two-stage calculus of variations and completion of squares techniques.