Automation and Remote Control

, Volume 79, Issue 7, pp 1207–1221 | Cite as

An Algorithm to Control Nonlinear Systems in Perturbations and Measurement Noise

  • I. B. FurtatEmail author
Nonlinear Systems


An algorithm was proposed to stabilize nonlinear systems with reduced level of impact of the measurement noise, parametric uncertainty, and external perturbation. Consideration was given to the noise of the measurements of dimensionality coinciding with that of the plant state vector. The parametric uncertainty and external perturbations can occur in any equation of the plant model. Conditions were obtained to calculate algorithm parameters in the form of solvability of the linear matrix inequality. Efficiency of the proposed scheme was illustrated by numerical examples.


nonlinear system compensation perturbation noise S-procedure linear matrix inequality 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Polyak, B.T. and Topunov, M.V., Suppression of Bounded Exogenous Disturbances: Output Feedback, Autom. Remote Control, 2008, vol. 69, no. 5, pp. 801–818.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Nikiforov, V.O., Nonlinear Control System with Compensation of the External Deterministic Disturbances, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1997, no. 4, pp. 69–73.Google Scholar
  3. 3.
    Fedele, G. and Ferrise, A., Biased Sinusoidal Disturbance Compensation with Unknown Frequency, IEEE Trans. Autom. Control, 2013, vol. 58, no. 12, pp. 3207–3212.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bukov, V.N., Vlozhenie sistem. Analiticheskii podkhod k analizu i sintezu matrichnykh sistem (System Embedding. An Analytical Approach to Analysis and Design of the Matrix Systems), Kaluga: Izd. Nauch. Lit. Bochkarevoi, 2006.Google Scholar
  5. 5.
    Proskurnikov, A.V. and Yakubovich, V.A., Universal Controllers in Problens of Optimal Control with Reference Model under Unknown External Signals, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2012, no. 2, pp. 49–62.Google Scholar
  6. 6.
    Tsykunov, A.M., Robastnoe upravlenie s kompensatsiei vozmushchenii (Robust Control with Perturbation Compensation), Moscow: Fizmatlit, 2012.Google Scholar
  7. 7.
    Guo, G., Hill, D.J., and Wang, Y., Nonlinear Output Stabilization Control for Multimachine Power Systems, IEEE Trans. Circuit. Syst. 1, 2000, vol. 47, no. 1, pp. 46–53.CrossRefGoogle Scholar
  8. 8.
    Chen, Y., Liu, F., Mei, S., and Ma, J., Toward Adaptive Robust State Estimation Based on MCC by Using the Generalized Gaussian Density as Kernel Functions, Electr. Power Energy Syst., 2015, vol. 71, pp. 297–304.CrossRefGoogle Scholar
  9. 9.
    Belyaev, A.N., Smolovik, S.V., Fradkov, A.L., and Furtat, I.B., Robust Control of Electrical Generator under Nonstationary Mechanical Power, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2013, no. 5, pp. 78–86.zbMATHGoogle Scholar
  10. 10.
    Metody robastnogo, neiro-nechetkogo i adaptivnogo upravleniya (Methods of Robust Neuro-Fuzzy and Adaptive Control), Egupov, N.D., Ed., Moscow: MTTU im. N.E. Baumana, 2002.Google Scholar
  11. 11.
    Baillieul, J., Feedback Coding for Information-Based Control: Operating Near the Data Rate Limit, in Proc. 41 IEEE Conf. Decision Control, ThP02-6, Las Vegas, Nevada, USA, 2002, pp. 3229–3236.Google Scholar
  12. 12.
    Delchamps, D.F., Extracting State Information from a Quantized Output Record, Syst. Control Lett., 1989, vol. 13, pp. 365–372.CrossRefzbMATHGoogle Scholar
  13. 13.
    Furtat, I.B., Fradkov, A.L., and Liberzon, D., Compensation of Disturbances for MIMO Systems with Quantized Output, Automatica, 2015, vol. 60, pp. 239–244.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Design of Control Laws Based on Linear Matrix Inequalities), Moscow: Fizmatlit, 2007.zbMATHGoogle Scholar
  15. 15.
    Polyak, B.T., Khlebnikov, M.V., and Shcherbakov, P.S., Upravlenie lineinymi sistemami pri vneshnikh vozmushcheniyakh. Tekhnika lineinykh matrichnykh neravenstv (Control of Linear Systems under External Perturbations. Technique of Linear Matrix Inequalities), Moscow: Lenand, 2014.Google Scholar
  16. 16.
    Furtat, I.B., Algorithm of Robust Control of Linear Plants with Vector Inputs-Outputs under Saturated Control Signal, Mekhatronika, Avtomatiz., Upravl., 2016, vol. 17, no. 9, pp. 579–587.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Fridman, E., A Refined Input Delay Approach to Sampled-data Control, Automatica, 2010, vol. 46, pp. 421–427.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.Google Scholar
  19. 19.
    Brammer, K. and Siffling, G., Kalman–Bucy-Filter: Deterministische Beobachtung und stochastische Filterung (Methoden der Regelungs-und Automatisierungstechnik), Wien: Oldenbourg, 1975. Translated under the title Determinirovannoe nablyudenie i stokhasticheskaya fil’tratsiya, Moscow: Nauka, 1982.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Problems of Mechanical Engineering Russian Academy of Sciences (IPME RAS)St. PetersburgRussia
  2. 2.ITMO University (National Research University of Information Technologies, Mechanics and Optics)St. PetersburgRussia

Personalised recommendations