Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay
This paper addresses the controller design problem for linear systems with time-varying delays. By constructing a novel Lyapunov–Krasovskii functional incorporating delay-partitioning techniques, we establish delay-dependent stability criteria for the solvability of the robust stabilization problem....
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-08-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/15/2519 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849770508614107136 |
|---|---|
| author | Hongli Yang Lijuan Yang Ivan Ganchev Ivanov |
| author_facet | Hongli Yang Lijuan Yang Ivan Ganchev Ivanov |
| author_sort | Hongli Yang |
| collection | DOAJ |
| description | This paper addresses the controller design problem for linear systems with time-varying delays. By constructing a novel Lyapunov–Krasovskii functional incorporating delay-partitioning techniques, we establish delay-dependent stability criteria for the solvability of the robust stabilization problem. The derived conditions are formulated as linear matrix inequalities (LMIs) that become affine upon fixing a single scalar parameter, thereby facilitating efficient numerical computation. Furthermore, these criteria guarantee that the reachable set of the closed-loop system remains bounded within a prescribed ellipsoid under zero initial conditions. The effectiveness and superiority of the proposed approach are demonstrated through two comparative numerical examples, including a benchmark problem with varying delay. |
| format | Article |
| id | doaj-art-54bafa46d33343cd83095b5643b84489 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-54bafa46d33343cd83095b5643b844892025-08-20T03:02:58ZengMDPI AGMathematics2227-73902025-08-011315251910.3390/math13152519Controller Design for Continuous-Time Linear Control Systems with Time-Varying DelayHongli Yang0Lijuan Yang1Ivan Ganchev Ivanov2College of Information Science and Technology, Qingdao Huanghai University, Linghai Road 1145, Qingdao 266427, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qianwangang Road 579, Qingdao 266590, ChinaFaculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 1000 Sofia, BulgariaThis paper addresses the controller design problem for linear systems with time-varying delays. By constructing a novel Lyapunov–Krasovskii functional incorporating delay-partitioning techniques, we establish delay-dependent stability criteria for the solvability of the robust stabilization problem. The derived conditions are formulated as linear matrix inequalities (LMIs) that become affine upon fixing a single scalar parameter, thereby facilitating efficient numerical computation. Furthermore, these criteria guarantee that the reachable set of the closed-loop system remains bounded within a prescribed ellipsoid under zero initial conditions. The effectiveness and superiority of the proposed approach are demonstrated through two comparative numerical examples, including a benchmark problem with varying delay.https://www.mdpi.com/2227-7390/13/15/2519time-delaycontroller designLyapunov–Krasovskii functionallinear matrix inequalityreachable set |
| spellingShingle | Hongli Yang Lijuan Yang Ivan Ganchev Ivanov Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay Mathematics time-delay controller design Lyapunov–Krasovskii functional linear matrix inequality reachable set |
| title | Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay |
| title_full | Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay |
| title_fullStr | Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay |
| title_full_unstemmed | Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay |
| title_short | Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay |
| title_sort | controller design for continuous time linear control systems with time varying delay |
| topic | time-delay controller design Lyapunov–Krasovskii functional linear matrix inequality reachable set |
| url | https://www.mdpi.com/2227-7390/13/15/2519 |
| work_keys_str_mv | AT hongliyang controllerdesignforcontinuoustimelinearcontrolsystemswithtimevaryingdelay AT lijuanyang controllerdesignforcontinuoustimelinearcontrolsystemswithtimevaryingdelay AT ivanganchevivanov controllerdesignforcontinuoustimelinearcontrolsystemswithtimevaryingdelay |