This paper investigates the stability problem of a class of discrete-time singularly perturbed Tagagi-Sugeno (T-S) fuzzy models. Stability conditions of reduced slow models, based on the use of Borne and Gentina practical stability criterion and matrices in the arrow form, are developed and compared with those concerning the initial singularly perturbed T-S system. The obtained results are practical and easy to use. An example is introduced to illustrate the proposed approaches.
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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