Receding horizon H^∞ tracking control for time-varying discrete linear systems

In this paper, a new receding horizon tracking control law based on the H control concept, is proposed for time-varying discrete linear systems. The proposed controller is constructed using a dynamic game approach minimizing a worst case finite horizon performance index with the finite terminal weighting matrix. The conditions on the terminal weighting matrix are proposed under which the proposed control law guarantees closed loop stability and, simultaneously, the infinite horizon H norm bound. It is shown that the proposed stability condition on the terminal weighting matrices can be converted to a Linear Matrix Inequality (LMI). In order to prove closed-loop stability, the monotonicity property of the cost is utilized instead of the monotonicity property of the Riccati equation. It is also shown that the proposed stability condition on both terminal weighting matrices and the cost horizon size are more general than the conventional results. Some examples are included to illustrate the proposed results.