H∞ optimal control over multiple Gilbert–Elliott type communication channels. (June 2021) - Mazumdar, Abhijit; Krishnaswamy, Srinivasan; Majhi, Somanath
Abstract: This paper considers the design of an H ∞ optimal controller for a linear time-invariant system over multiple Gilbert–Elliott type lossy communication channels. The problem is formulated as a two-player zero-sum game. For the finite horizon case, we have derived conditions that ensure the existence of a unique saddle-point. Further, the value of the game along with the corresponding optimal input and optimal disturbance trajectories are obtained. These results have then been extended to the infinite horizon case. It has been shown that if a unique saddle-point exists then the optimal control law stabilizes the system while the L 2 gain from the disturbance input to the controlled output will be less than or equal to certain γ > 0 .