Abstract
The guardian map theory of generalized stability of parametrized linear time-invariant systems is used to prove new results on stability of linear time-invariant singularly perturbed systems. The results give necessary and sufficient conditions for generalized stability of the perturbed system for all sufficiently small values of the singular perturbation parameter, and, moreover, yield the exact parameter range for stability. Thus, the results generalize significantly the classical Klimushev-Krasovskii Theorem, while at the same time providing closed-form expressions for the maximal parameter range for stability.
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© 1990 Birkhäuser Boston
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Abed, E.H., Saydy, L., Tits, A.L. (1990). Generalized Stability of Linear Singularly Perturbed Systems Including Calculation of Maximal Parameter Range. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4484-4_17
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DOI: https://doi.org/10.1007/978-1-4612-4484-4_17
Publisher Name: Birkhäuser Boston
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