Automation and Remote Control

, Volume 80, Issue 11, pp 1976–1995 | Cite as

State Estimation and Stabilization of Discrete-Time Systems with Uncertain Nonlinearities and Disturbances

  • A. I. MalikovEmail author
Nonlinear Systems


Nonautonomous discrete-time control systems with uncertain nonlinearities and bounded external disturbances are considered. Based on the method of matrix comparison systems and the technique of difference linear matrix inequalities, an approach to solve the problems of state estimation, finite time boundedness with respect to given sets, the suppression of initial deviations and uncertain disturbances using a linear state feedback controller is developed. A method to design a controller with variable coefficients that guarantees the transition from one given ellipsoid to another under any disturbances bounded by the L norm is proposed.


nonautonomous discrete-time systems with Lipschitz nonlinearities uncertain disturbances state estimation finite time boundedness controller design 


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This work was supported in part by the Russian Foundation for Basic Research, project no. 18- 08-01045a (Sections 2–4) and by RAS Basic Research Programs no. 7 “New Developments in Promising Areas of Energy, Mechanics and Robotics” (Sections 5 and 6).


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Tupolev National Research Technical University (KAI)KazanRussia
  2. 2.Institute of Mechanics and Engineering, Kazan Research CenterRussian Academy of SciencesKazanRussia

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