Abstract:In this paper, a constructive design methodology for Finite-Time Stability (FTS) of a class of nonlinear discrete-time systems is proposed. A dead-beat controller that can achieve n-finite-time stability is constructed. Furthermore, stability conditions, based on the use of Borne and Gentina practical stability criterion and matrices in the Benrejeb arrow form, are synthesized. Similarity between transient behaviors of dead-beat controlled linearized and nonlinear third order systems are shown and concluding remarks are formulated.

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In this paper, the impact of the discretization techniques and the sampling time, on the finite-time stabilization of sampled-data controlled Linear Time Invariant (LTI) systems, is investigated. To stabilize the process in finite time, a discretetime feedback dead-beat controller is designed for the sampleddata system. Checkable conditions on the approximate discretetime plant model and the associated controller that guarantee the finite-time stabilization of the exact model are developed. The trade-off between the discretization technique, the sampling time and the desired performances is illustrated and discussed. Results are presented through a case study.

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