“How to Drive a Delayed Response, Stochastic System Close to Equilibrium”

Authors: Sjur D. Flåm,
Affiliation: Christian Michelsen Research
Reference: 1983, Vol 4, No 2, pp. 95-100.

Keywords: Stability, control, stochastic system, delayed differential equation

Abstract: We consider a continuous system that, in the absence of random perturbations and external forcing, is uniformly, asymptotically stable in a global sense. The system evolution is governed by a retarded differential equation. To this equation is added unidentified, time- and state-dependent noise. However, in each instance the noise is bounded over the probability space. We demonstrate that approximate stability is obtainable by a deterministic approach based on worst case analysis.

PDF PDF (1151 Kb)        DOI: 10.4173/mic.1983.2.3

References:
[1] BARMISH, B.R. (1982). Global and point controllability of uncertain dynamical systems, IEEE Trans. on Automatic Control, 27, 399-407 doi:10.1109/TAC.1982.1102925
[2] CORLESS, M.J., LEITMANN, G. (1981). Continuous state feedback guaranteeing uniform, ultimate boundedness for uncertain dynamic systems, IEEE Trans. on Automatic Control, 26, 1139-1144 doi:10.1109/TAC.1981.1102785
[3] CUSHING, J.M. (1980). Stability and maturation periods in age-structured populations, In Differential Equations and Applications in Ecology, Epidemics and Population Problems, Ed. Busenberg and Cooke.New York : Academic Press.
[4] GUTMAN, S. (1979). Uncertain dynamical systems - A Lyapunov min-max approach, IEEE Trans. on Automatic Control, 24, 437-443 doi:10.1109/TAC.1979.1102073
[5] HALE, J. (1977). Theory of functional differential equations, New York : Springer-Verlag.
[6] LEITMANN, G. (1981). On the efficacy of non-linear control in uncertain linear systems, Journal of Dynamical Systems, Measurement and Control, 102, 95-102.


BibTeX:
@article{MIC-1983-2-3,
  title={{How to Drive a Delayed Response, Stochastic System Close to Equilibrium}},
  author={Flåm, Sjur D.},
  journal={Modeling, Identification and Control},
  volume={4},
  number={2},
  pages={95--100},
  year={1983},
  doi={10.4173/mic.1983.2.3},
  publisher={Norwegian Society of Automatic Control}
};