Control of systems with aftereffect in scales of linear controllers with respect to the type of feedback. (English. Russian original) Zbl 1246.93046
Differ. Equ. 47, No. 7, 1014-1028 (2011); translation from Differ. Uravn. 47, No. 7, 1003-1017 (2011).
The modal control problem, which arose when solving applied problems, is one of the most important problems of synthesis linear control systems with deviating argument. In this paper, the modal stabilization and modal control problem for delay systems in scales of linear controllers with aftereffect are considered. Difference and integral controllers have been considered. For the reviewer is not clear why eq.(3) generalize eq.(2), eq.(6) and the equation in the next line of this text are generalizations one another. It is not clear how was obtained eq. (7).
Reviewer: Yuri N. Sankin (Ul’yanovsk)
MSC:
| 93B50 | Synthesis problems |
| 93D15 | Stabilization of systems by feedback |
| 93C05 | Linear systems in control theory |
Keywords:
modal control problem; linear control systems; deviating argument; delay systems; aftereffect; difference and integral controllersReferences:
| [1] | Krasovskii, N.N. and Osipov, Yu.S., On the Stabilization of Motions of a Plant with Delays in the Control System, Izv. Akad. Nauk SSSR Tehn. Kibernet., 1963, no. 6, pp. 3–15. · Zbl 1122.93402 |
| [2] | Osipov, Yu.S., On the Stabilization of Control Systems with Delay, Differ. Uravn., 1965, vol. 1, no. 5, pp. 606–618. · Zbl 0163.10902 |
| [3] | Gabelaya, A.G., Ivanenko, V.I., and Odarich, O.N., Stabilization of Linear Autonomous Control Systems, Kibernetika, 1975, no. 3, pp. 69–72. |
| [4] | Pandolfi, L., Stabilization of Neutral Functional-Differential Equations, J. Optim. Theory Appl., 1976, vol. 20, pp. 191–204. · Zbl 0313.93023 · doi:10.1007/BF01767451 |
| [5] | Olbrot, A.W., Stabilizability, Detectability and Spectrum Assignment for Linear Autonomous Systems with General Time Delays, IEEE Trans. Automat. Control, 1978, vol. AC-23, pp. 887–890. · Zbl 0399.93008 · doi:10.1109/TAC.1978.1101879 |
| [6] | Watanabe, K., Stabilization of Linear Systems with Non-Commensurate Delays, Internat. J. Control, 1988, vol. 48, no. 81, pp. 333–342. · Zbl 0647.93059 · doi:10.1080/00207178808906179 |
| [7] | Borkovskaya, I.M. and Marchenko, V.M., On an Approach to the Problem of the Stabilization of Systems with Delay, Prikl. Mat. Mekh., 1996, vol. 60, no. 4, pp. 531–541. · Zbl 0890.93073 |
| [8] | Rabah, R., Sklyar, G.M., and Rezounenko, A.V., On Strong Stability and Stabilizability of Linear Systems of Neutral Type, Adv. Time-Delay Systems, Berlin, 2004, pp. 257–268. · Zbl 1060.34051 |
| [9] | Marchenko, V.M. and Yakimenko, A.A., On the Stabilizing Controller Design for Delay Systems of Neutral Type, Differ. Uravn., 2007, vol. 43, no. 11, pp. 1480–1486. · Zbl 1180.93090 |
| [10] | Letov, A.M., Analytic Construction of Controllers, Avtomat. i Telemekh., 1960, no. 4, pp. 436–441; no. 5, pp. 561–568; no. 6, pp. 661–665; 1961, no. 4, pp. 425–435. |
| [11] | Rosenbrock, H.H., Distinctive Problems of Process Control, Chem. Engng. Progr., 1962, vol. 58, no. 9, pp. 43–50. |
| [12] | Wonham, W.M., On Pole Assignment in Multi-Input Controllable Systems, IEEE Trans. Automat. Control, 1967, vol. AC-12, no. 6, pp. 660–665. · doi:10.1109/TAC.1967.1098739 |
| [13] | Porter, B. and Grossley, T.R., Modal Control, London, 1972. |
| [14] | Kuzovkov, N.T., Modal’noe upravlenie i nablyudayushchie ustroistva (Modal Control and Observing Devices), Moscow, 1976. |
| [15] | Andreev, Yu.N., Algebraic State Space Methods in Linear Plant Control Theory (Survey of Foreign Literature), Avtomat. i Telemekh., 1977, no. 3, pp. 5–50. |
| [16] | Bulatov, V.I., Kalyuzhnaya, T.S., and Naumovich, R.F., Control of the Spectrum of Differential Equations, Differ. Uravn., 1974, vol. 10, no. 11, pp. 1946–1952. |
| [17] | Morse, A.S., Ring Models for Delay-Differential Systems, Automatica, 1976, vol. 12, no. 5, pp. 529–531. · Zbl 0345.93023 · doi:10.1016/0005-1098(76)90013-3 |
| [18] | Asmykovich, I.K. and Marchenko, V.M., Spectrum Control in Systems with Delay, Avtomat. i Telemekh., 1976, no. 7, pp. 5–14. · Zbl 0386.93038 |
| [19] | Marchenko, V.M., On the Problem of Modal Control in Linear Systems with Delays, Dokl. Akad. Nauk BSSR, 1978, vol. 22, no. 5, pp. 401–404. · Zbl 0379.93021 |
| [20] | Watanabe, K., Finite Spectrum Assignment of Linear Systems with a Class of Noncommensurate Delays, Internat. J. Control, 1987, vol. 47, no. 5, pp. 1277–1289. · Zbl 0641.93032 · doi:10.1080/00207178808906095 |
| [21] | Marchenko, V.M., Modal Control in Systems with Aftereffect, Avtomat. i Telemekh., 1988, no. 11, pp. 73–83. |
| [22] | Gorecki, H., Fuksa, S., Grabowski, P., and Korytowski, A., Analysis and Synthesis of Time Delay Systems, Warszawa, 1989. · Zbl 0695.93002 |
| [23] | Borkovskaya, I.M. and Marchenko, V.M., Modal Control of Systems with Distributed Delay under Incomplete Information Conditions, Differ. Uravn., 1993, vol. 29, no. 11, pp. 1928–1936. · Zbl 0815.93065 |
| [24] | Marchenko, V.M. and Yakimenko, A.A., On the Modal Control of Multi-Input Systems with Retarded Argument of Neutral Type, Differ. Uravn., 2008, vol. 44, no. 11, pp. 1534–1543. · Zbl 1157.93013 |
| [25] | Kalman, R., Falb, P., and Arbib, M., Topics in Mathematical System Theory, New York: McGraw-Hill, 1969. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: Mir, 1971. · Zbl 0231.49001 |
| [26] | Kamen, E.W., Linear Systems with Commensurate Time Delays: Stability and Stabilization Independent of Delay, IEEE Trans. Automat. Control, 1982, vol. AC-27, no. 2, pp. 367–375. · Zbl 0517.93047 · doi:10.1109/TAC.1982.1102916 |
| [27] | Datko, R., Remarks Concerning the Asymptotic Stability and Stabilization of Linear Delay Differential Equations, Math. Anal. Appl., 1985, vol. 111, no. 2, pp. 571–584. · Zbl 0579.34052 · doi:10.1016/0022-247X(85)90236-7 |
| [28] | Filimonov, A.B., Controlling the Spectrum of Linear Stationary Objects with Lags, Avtomat. i Telemekh., 1983, no. 4, pp. 34–42. · Zbl 0552.93005 |
| [29] | Shilov, G.E., Matematicheskii analiz. Spetsial’nyi Kurs (Mathematical Analysis. Special Course), Moscow, 1960. |
| [30] | Pearson, J.B. and Ding, C.Y., Compensator Design for Multivariable Linear Systems, IEEE Trans. Automat. Control, 1985, vol. AC-14, no. 2, pp. 130–134. |
| [31] | El’sgol’ts, L.E. and Norkin, S.B., Vvedenie v teoriyu differentsial’nykh uravnenii s otklonyayushchimsya argumentom (Introduction to the Theory of Differential Equations with Deviating Argument), Moscow: Nauka, 1971. |
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