Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE

Yan Zhang, D. Subbaram Naidu, Chenxiao Cai and Yun Zou

International Journal of Systems Science, 2016, vol. 47, issue 11, 2632-2641

Abstract: In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.

Date: 2016
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DOI: 10.1080/00207721.2015.1006710

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