Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls
Abstract This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and distributed time-varying delays, but not necessarily differentiable. The proposed co...
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2018-11-01
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Online Access: | http://link.springer.com/article/10.1186/s13662-018-1898-y |
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doaj-6612e4d3f2e94a1b96778252de30a8bb2020-11-25T01:32:27ZengSpringerOpenAdvances in Difference Equations1687-18472018-11-012018112310.1186/s13662-018-1898-yGuaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controlsNuchira Khongja0Thongchai Botmart1Piyapong Niamsup2Wajaree Weera3Department of Mathematics, Khon Kaen UniversityDepartment of Mathematics, Khon Kaen UniversityDepartment of Mathematics, Chiang Mai UniversityDepartment of Mathematics, University of Pha YaoAbstract This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and distributed time-varying delays, but not necessarily differentiable. The proposed conditions allow us to design the state feedback controllers which stabilize the closed-loop system. By constructing an appropriate Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for the existence of guaranteed cost control are given in terms of linear matrix inequalities (LMIs). Moreover, we design new quadratic cost functions and minimize their upper bound. Finally, numerical examples are given to illustrate the effectiveness and improvement over some existing results in the literature.http://link.springer.com/article/10.1186/s13662-018-1898-yGuaranteed cost controlExponential stabilityMixed time-varying delaysFeedback control |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nuchira Khongja Thongchai Botmart Piyapong Niamsup Wajaree Weera |
spellingShingle |
Nuchira Khongja Thongchai Botmart Piyapong Niamsup Wajaree Weera Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls Advances in Difference Equations Guaranteed cost control Exponential stability Mixed time-varying delays Feedback control |
author_facet |
Nuchira Khongja Thongchai Botmart Piyapong Niamsup Wajaree Weera |
author_sort |
Nuchira Khongja |
title |
Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls |
title_short |
Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls |
title_full |
Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls |
title_fullStr |
Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls |
title_full_unstemmed |
Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls |
title_sort |
guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2018-11-01 |
description |
Abstract This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and distributed time-varying delays, but not necessarily differentiable. The proposed conditions allow us to design the state feedback controllers which stabilize the closed-loop system. By constructing an appropriate Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for the existence of guaranteed cost control are given in terms of linear matrix inequalities (LMIs). Moreover, we design new quadratic cost functions and minimize their upper bound. Finally, numerical examples are given to illustrate the effectiveness and improvement over some existing results in the literature. |
topic |
Guaranteed cost control Exponential stability Mixed time-varying delays Feedback control |
url |
http://link.springer.com/article/10.1186/s13662-018-1898-y |
work_keys_str_mv |
AT nuchirakhongja guaranteedcostcontrolforexponentialstabilityofanonlinearsystemwithmixedtimevaryingdelaysinstatesandcontrols AT thongchaibotmart guaranteedcostcontrolforexponentialstabilityofanonlinearsystemwithmixedtimevaryingdelaysinstatesandcontrols AT piyapongniamsup guaranteedcostcontrolforexponentialstabilityofanonlinearsystemwithmixedtimevaryingdelaysinstatesandcontrols AT wajareeweera guaranteedcostcontrolforexponentialstabilityofanonlinearsystemwithmixedtimevaryingdelaysinstatesandcontrols |
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1725082046925111296 |