Robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays via sliding mode approach.

In this paper, the issue of robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays is investigated via sliding mode control (SMC). A sliding mode strategy is presented combined with the observer technique, since the system states are unmeasured. The distinguishing feature of the provided strategy is that a novel sliding surface is constructed based upon the estimated states such that the resulting full-order closed-loop system is generated. Furthermore, by employing Lyapunov-Krasovskii functional, new sufficient criteria in terms of a solvable linear matrix inequality (LMI) is derived, insuring that the closed-loop system is admissible with an H∞-norm bound. With the solution of the LMI, a corresponding sliding mode controller is obtained for reaching motion and reducing the chattering. At last, the theoretical results are verified in numerical tests.