An approach to the problem of stabilizing systems with delay.

*(English. Russian original)*Zbl 0890.93073
J. Appl. Math. Mech. 60, No. 4, 529-539 (1996); translation from Prikl. Mat. Mekh. 60, No. 4, 531-541 (1996).

Servo systems describable by linear ODE’s with constant delay are considered. The problem consists of designing a linear feedback network with delay (the controller) to render the system stable. Stability corresponds to the real parts of all eigenvalues being negative. The type of feedback network and the “free parameters” are chosen accordingly. The Wiener-Paley theorem on non-quasianalytic functions and its implications on the frequency response are used to exclude networks which are non-realizable (within the framework of linear theory).

The publication is of interest mainly to ‘system engineers’.

The publication is of interest mainly to ‘system engineers’.

Reviewer: I.Gumowski (Thoiry)

##### MSC:

93D15 | Stabilization of systems by feedback |

34K35 | Control problems for functional-differential equations |

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\textit{I. M. Borkovskaya} and \textit{V. M. Marchenko}, J. Appl. Math. Mech. 60, No. 4, 529--539 (1996; Zbl 0890.93073); translation from Prikl. Mat. Mekh. 60, No. 4, 531--541 (1996)

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##### References:

[1] | Krasovskii, N.N.; Osipov, Yu.S., Stabilization of the motions of a controlled system with delay in a regulation system, Izv. akad. nauk SSSR. tekh. kibernetika, 6, 3-15, (1963) · Zbl 1122.93402 |

[2] | Osipov, Yu.S., Stabilization of controlled systems with delay, Diff. uravneniya, 1, 5, 605-618, (1965) · Zbl 0163.10902 |

[3] | Shimanov, S.N., The theory of linear differential systems with aftereffect, Diff. uravneniya, 1, 1, 102-116, (1965) · Zbl 0196.46201 |

[4] | Morse, A.S., Ring models for delay-differential systems, Automatica, 12, 5, 529-531, (1976) · Zbl 0345.93023 |

[5] | Asmykovich, I.K.; Marchenko, V.M., Control of the spectrum of systems with delay, Avtomatika i telemekhanika, 7, 5-14, (1976) · Zbl 0386.93038 |

[6] | Datko, R., Remarks concerning the asymptotic stability and stabilization of linear delay differential equations, Math. anal. appl., 111, 2, 571-584, (1985) · Zbl 0579.34052 |

[7] | Marchenko, V.M., The problem of modal control in linear systems with delay, Dokl akad. nauk BSSR, 22, 5, 401-404, (1978) · Zbl 0379.93021 |

[8] | Kamen, E.W., Linear systems with commensurate time delays: stability and stabilization independent of delay, IEEE trans. aut. control, AC-27, 2, 367-375, (1982) · Zbl 0517.93047 |

[9] | Marchenko, V.M., Modal control in systems with aftereffect, Avtomatika i telemekhanika, 11, 73-83, (1988) |

[10] | Pandolfi, L., Stabilization of neutral functional differential equations, J. optimiz theory appl., 20, 2, 191-204, (1976) · Zbl 0313.93023 |

[11] | Olbrot, A.W., Stabilizability, detectability and spectrum assignment for linear autonomous systems with general time delays, IEEE turns. aut. control, AC-23, 5, 887-890, (1978) · Zbl 0399.93008 |

[12] | Watanabe, E., Finite spectrum assignment of linear systems with a class of noncommensurate delays, Int. J. control., 47, 5, 1277-1289, (1988) · Zbl 0641.93032 |

[13] | Gabelaya, A.G.; Ivanenko, V.I.; Odarich, O.N., The stabilizability of linear autonomous systems with delay, Automatica i telemekhanika, 8, 12-16, (1976) |

[14] | El’Sgol’ts, L.E.; Norkin, S.B., Introduction to the theory of differential equations with divergent argument, (1971), Nauka Moscow · Zbl 0224.34053 |

[15] | Shilov, G.Ye., Mathematical analysis. A special course, (1960), Fizmatgiz Moscow |

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