DOI: 10.17586/2226-1494-2016-16-4-627-634


T. A. Kharkovskaia, A. S. Kremlev, D. V. Efimov

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Article in Russian

For citation: Kharkovskaia T.A., Kremlev A.S., Efimov D.V. Interval state estimation for singular differential equation systems with delays. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 4, pp. 627–634. doi: 10.17586/2226- 1494-2016-16-4-627-634


The paper deals with linear differential equation systems with algebraic restrictions (singular systems) and a method of interval observer design for this kind of systems. The systems contain constant time delay, measurement noise and disturbances. Interval observer synthesis is based on monotone and cooperative systems technique, linear matrix inequations, Lyapunov function theory and interval arithmetic. The set of conditions that gives the possibility for interval observer synthesis is proposed. Results of synthesized observer operation are shown on the example of dynamical interindustry balance model. The advantages of proposed method are that it is adapted to observer design for uncertain systems, if the intervals of admissible values for uncertain parameters are given. The designed observer is capable to provide asymptotically definite limits on the estimation accuracy, since the interval of admissible values for the object state is defined at every instant. The obtained result provides an opportunity to develop the interval estimation theory for complex systems that contain parametric uncertainty, varying delay and nonlinear elements. Interval observers increasingly find applications in economics, electrical engineering, mechanical systems with constraints and optimal flow control.

Keywords: interval estimation, observer, singular systems, time delay, uncertain systems

Acknowledgements. This work was supported by the Government of the Russian Federation (Grant 074-U01), the Ministry of Education and Science of the Russian Federation (Project 14.Z50.31.0031) and the Russian Federation President Grant №14.Y31.16.9281-НШ.


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