Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay

Hongli Yang, Lijuan Yang and Ivan Ganchev Ivanov ()
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Hongli Yang: College of Information Science and Technology, Qingdao Huanghai University, Linghai Road 1145, Qingdao 266427, China
Lijuan Yang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qianwangang Road 579, Qingdao 266590, China
Ivan Ganchev Ivanov: Faculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 1000 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 15, 1-11

Abstract: 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.

Keywords: time-delay; controller design; Lyapunov–Krasovskii functional; linear matrix inequality; reachable set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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