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.
Bibliographical noteFunding Information:
The authors would like to thank the Associate Editor and five anonymous reviewers for their valuable comments and suggestions that certainly improved the quality of this article.This work was supported jointly by the China Scholarship Council and National Natural Science Foundation of China [grant number 61104064], [grant number 61174038].
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- Asymptotically stability
- Composite control
- Discrete-time nonlinear singularly perturbed systems
- Optimal control
- State-dependent Riccati equation