article · SIAM Journal on Control and Optimization · 1992
On the Exponential Stability of Singularly Perturbed Systems
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Abstract
This paper establishes some results and properties related to the exponential stability of general dynamical systems and, in particular, singularly perturbed systems. For singularly perturbed systems it is shown that if both the reduced-order system and the boundary-layer system are exponentially stable, then, provided that some further regularity conditions are satisfied, the full-order system is exponentially stable for sufficiently small values of the perturbation parameter $\mu $, and its rate of convergence approaches that of the reduced-order system $(\mu = 0)$ as $\mu $ approaches zero. Exponentially decaying norm bounds are given for the “slow” and “fast” components of the full-order system trajectories. To achieve this result, a new converse Lyapunov result for exponentially stable systems is presented.
Cite this paper
Corless, M., & Glielmo, L. (1992). On the Exponential Stability of Singularly Perturbed Systems. SIAM Journal on Control and Optimization, 30(6), 1338–1360. https://doi.org/10.1137/0330071
Corless, M., and Luigi Glielmo. “On the Exponential Stability of Singularly Perturbed Systems.” SIAM Journal on Control and Optimization, vol. 30, no. 6, 1992, pp. 1338–60, https://doi.org/10.1137/0330071.
Corless, M., and Luigi Glielmo. 1992. “On the Exponential Stability of Singularly Perturbed Systems.” SIAM Journal on Control and Optimization 30 (6): 1338–60. https://doi.org/10.1137/0330071.
Corless, M. and Glielmo, L. (1992) ‘On the Exponential Stability of Singularly Perturbed Systems’, SIAM Journal on Control and Optimization, 30(6), pp. 1338–1360. Available at: https://doi.org/10.1137/0330071.
@article{corless1992exponential,
title = {{On the Exponential Stability of Singularly Perturbed Systems}},
author = {Corless, M. and Glielmo, Luigi},
journal = {SIAM Journal on Control and Optimization},
volume = {30},
number = {6},
pages = {1338--1360},
year = {1992},
doi = {10.1137/0330071}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.