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A new discrete sliding mode control for systems with time varying delay: Multi-Structure approach

Modeling the discrete-time systems with time varying delay had several difficulties, such as, the determination of an adequate model describing the real output evolution. Also, controlling such systems is another problem to be resolved. In this paper, we propose a Multi-Structure approach for modeling and controlling discrete-time systems with time-varying delay. With knowledge about upper and lower bound of the delay term, we generate a systematic model base reproducing the real output evolution. Then, a Multi-Structure Discrete Sliding Mode Control scheme (MS-DSMC) was developed to stabilize such systems. In this new strategy, a delay independent sufficient condition for the existence of stable sliding surface was given in terms of linear matrix inequalities (LMIs). The effectiveness of this new method was illustrated through numerical example.