Abstract
The purpose of this paper is to present the concept of parametric stability of dynamic systems, which provides a mathematical framework for solving the joint problem of feasibility and stability of equilibrium states. This problem arises whenever uncertain parameters can cause the equilibrium states to shift or disappear altogether, thus making the analysis of robust stability misleading or useless. In particular, we establish conditions for parametric stability in the context of Liapunov’s Direct Method and study in some detail the generalized Lotka-Volterra equations, which have been recently introduced as models for artificial neural networks.
Keywords
- Uncertain Parameter
- Parametric Stability
- Intrinsic Growth Rate
- Interconnected System
- Structural Perturbation
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© 1991 Springer Science+Business Media New York
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Ikeda, M., Ohta, Y., Šiljak, D.D. (1991). Parametric Stability. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_1
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DOI: https://doi.org/10.1007/978-1-4612-0439-8_1
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6760-7
Online ISBN: 978-1-4612-0439-8
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