STABILIZATION OF A SCALAR EQUATION WITH DELAY IN THE STATE AND CONTROL VARIABLES

被引：0

作者：

Shayakhmetova, L., V ^{[1
]}

Kharitonov, V. L. ^{[1
]}

机构：

[1] St Petersburg State Univ, 7-9 Univ Skaya Embankment, St Petersburg 199034, Russia

来源：

VESTNIK SANKT-PETERBURGSKOGO UNIVERSITETA SERIYA 10 PRIKLADNAYA MATEMATIKA INFORMATIKA PROTSESSY UPRAVLENIYA | 2014年 / 10卷 / 04期

关键词：

time-delay systems; stabilization;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The contribution is dedicated to the stabilization problem of systems with input and state delay. We derive a stabilizing control law for the case of a scalar equation with several state and two input delays. We start with a control law of the form, where the right hand side contains future values of the state predicted by Cauchy formula. The presented control law is of the form of an integral equation. It is shown that the characteristic function of the closed-loop system consists of two factors. Special conditions that guarantee the exponential stability of the closed-loop system are derived. Exponential estimates for the solutions of the closed-loop system are given. An illustrative example is presented.

引用

页码：144 / 151

页数：8

共 9 条

[1] [Anonymous], 2013, TIME DELAY SYSTEMS
[2] [Anonymous], 1946, AUTOMAT REM CONTR+
[3] Stabilization of linear strict-feedback systems with delayed integrators
Bekiaris-Liberis, Nikolaos
Krstic, Miroslav
[J]. AUTOMATICA, 2010, 46 (11) : 1902 - 1910
[4] Bellman RKL, 1963, DIFFERENTIAL DIFFERE, DOI 10.1063/1.3050672
[5] An extension of the prediction scheme to the case of systems with both input and state delay
Kharitonov, Vladimir L.
[J]. AUTOMATICA, 2014, 50 (01) : 211 - 217
[6] Krstic M, 2009, SYST CONTROL-FOUND A, P1, DOI 10.1007/978-0-8176-4877-0
[7] FINITE SPECTRUM ASSIGNMENT PROBLEM FOR SYSTEMS WITH DELAYS
MANITIUS, AZ
OLBROT, AW
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1979, 24 (04) : 541 - 553
[8] Michiels W, 2007, ADV DES CONTROL, P3
[9] Shayakhmetova L. V., 2014, CONTROL PROCESSES ST, V1, P70

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