Abstract
We propose a solution for the modal controllability problem for linear autonomous differential systems of neutral type with commensurate delays in two classes of differentialdifference controllers.
Similar content being viewed by others
References
Manitius, A.Z. and Olbrot, A.W., Finite Spectrum Assignment Problem for Systems with Delays, IEEE Trans. Autom. Control, 1979, AC-24, no. 4, pp. 541–553.
Watanabe, K., Finite Spectrum Assignment of Linear Systems with a Class of Noncommensurate Delays, Int. J. Control, 1987, vol. 47, no. 5, pp. 1277–1289.
Wang, Q.G., Lee, T.H., and Tan, K.K., Finite Spectrum Assignment Controllers for Time Delay Systems, London: Springer, 1995.
Metel’skii, A.V., Finite Spectrum Assignment Problem for a Differential Systems of Neutral Type, Differ. Uravn., 2015, vol. 51, no. 1, pp. 70–83.
Krasovskii, N.N. and Osipov, Yu.S., On Stabilization of the Motion of a Controllable Object with Delay in a Control System, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1963, no. 6, pp. 3–15.
Osipov, Yu.S., On Stabilization of Controllable Systems with Delay, Differ. Uravn., 1965, vol. 1, no. 5, pp. 606–618.
Marchenko, V.M., Control of Systems with Aftereffect in Scales of Linear Controllers with Respect to the Type of Feedback, Differ. Uravn., 2011, vol. 47, no. 7, pp. 1003–1017.
Minyaev, S.I. and Fursov, A.S., Simultaneous Stabilization: Construction of a Universal Stabilizer for Linear Plants with Delay with the Use of Spectral Reducibility, Differ. Uravn., 2012, vol. 48, no. 11, pp. 1533–1539.
Kharitonov, V.L., An Extension of the Prediction Scheme to the Case of Systems with Both Input and State Delay, Automatica, 2014, vol. 50, pp. 211–217.
Pandolfi, L., Stabilization of Neutral Functional-Differential Equations, J. Optim. Theory Appl., 1976, vol. 20, pp. 191–204.
Lu, W.-S., Lee, E., and Zak, S., On the Stabilization of Linear Neutral Delay-Difference Systems, IEEE Trans. Autom. Control, 1986, vol. 31, no. 1, pp. 65–67.
Rabah, R., Sklyar, G.M., and Rezounenko, A.V., On Strong Stability and Stabilizability of Linear Systems of Neutral Type, in Advanced in Time-Delay Systems, Berlin: Springer, 2004, pp. 257–268.
Gu, K., A Review of Some Subtleties of Practical Relevance for Time Delay Systems of Neutral Type, ISRN Appl. Math., 2012, Article ID 725783, 46 p.
Pavlovskaya, A.T. and Khartovskii, V.E., Control of Linear Systems with Delay of Neutral Type with Controllers with Dynamical Structure Feedback, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2014, no. 3, pp. 3–18.
Metel’skii, A.V. and Khartovskii, V.E., Criteria for Modal Controllability of Linear Systems of Neutral Type, Differ. Uravn., 2016, vol. 52, no. 11, pp. 1506–1521.
Khartovskii, V.E., Spectral Reduction of Linear Systems of the Neutral Type, Differ. Uravn., 2017, vol. 53, no. 3, pp. 375–390.
Marchenko, V.M. and Yakimenko, A.A., On Modal Control of Multiinput Systems with Delayed Argument of Neutral Type, Differ. Uravn., 2008, vol. 44, no. 11, pp. 1534–1543.
Metel’skii, A.V., Complete Stopping and Stabilization of Systems with Delay via Spectral Reduction, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2014, no. 1, pp. 3–11.
Metel’skii, A.V., Khartovskii, V.E., and Urban, O.I., Solution Damping Controllers for Linear Systems of the Neutral Type, Differ. Uravn., 2016, vol. 52, no. 3, pp. 391–403.
Metel’skii, A.V., Khartovskii, V.E., and Urban, O.I., Damping of a Solutions of Differential Systems with Multiple Delays via Feedback, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2015, no. 2, pp. 40–50.
Engelborghs, K., Dambrine, M., and Roos, D., Limitation of a Class of Stabilization Methods for Delay Systems, IEEE Trans. Autom. Control, 2001, vol. 64, pp. 336–339.
Emel’yanov, S.V., Fomichev, V.V., and Fursov, A.S., Simultaneous Stabilization of Linear Dynamic Plants by the Variable-Structure Controller, Autom. Remote Control, 2012, vol. 73, no. 7, pp. 1126–1133.
Khartovskii, V.E. and Pavlovskaya, A.T., Complete Controllability and Controllability for Linear Autonomous Systems of Neutral Type, Autom. Remote Control, 2013, vol. 74, no. 5, pp. 769–784.
Khartovskii, V.E., A Generalization of the Complete Controllability Problems for Differential Systems with Commensurate Delays, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2009. no. 6, pp. 3–11.
Il’in, A.V., Budanova, A.V., and Fomichev, V.V., Observers for Systems with Delay under External Noise, Dokl. Akad. Nauk, 2014, vol. 456, no. 1, pp. 27–31.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.E. Khartovskii, 2017, published in Avtomatika i Telemekhanika, 2017, No. 11, pp. 3–19.
Rights and permissions
About this article
Cite this article
Khartovskii, V.E. Modal controllability for systems of neutral type in classes of differential-difference controllers. Autom Remote Control 78, 1941–1954 (2017). https://doi.org/10.1134/S0005117917110017
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117917110017