New stability conditions for discrete singularly perturbed systems are presented in this study. The corresponding slow and fast subsystems of the original discrete singularly perturbed system are first derived. The observer-based controllers for the slow and the fast subsystems are then separately designed and a composite observer-based controller for the original system is subsequently synthesized from these observer-based controllers. Finally, a frequency domain ε-dependent stability criterion for the original discrete singularly perturbed system under the composite observer-based controller is proposed. If any one condition of this criterion is fulfilled, stability of the original system by establishing that of its corresponding slow and fast subsystems is thus investigated. An illustrative example is given to demonstrate that the upper bound of the singular perturbation parameter ε can be obtained by examining this criterion.
Stabilization of Discrete Singularly Perturbed Systems Under Composite Observer-Based Control
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received by the Dynamic Systems and Control Division February 2, 1999. Associate Technical Editor: B. Siciliano.
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Hsiao, F., Hwang, J., and Pan, S. (February 2, 1999). "Stabilization of Discrete Singularly Perturbed Systems Under Composite Observer-Based Control." ASME. J. Dyn. Sys., Meas., Control. March 2001; 123(1): 132–139. https://doi.org/10.1115/1.1285759
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