Variable Structure Controller for Stabilizing Delayed Systems: A Lyapunov-Krasovskii Design Approach
Ringo RIMBE, Raidandi DANWE, Irépran DAMAKOA, Edwin Nyuysever MBINKAR

Abstract
A Variable Structure Controller (VSC) is designed for the purpose of stabilizing a Time Delay System (TDS). The considered system is delay-dependent stable. The system remains stable as delay is increased from zero to a maximum value at which stability is then lost. Using a memoryless stabilization feedback, a sliding surface is constructed through a Lyapunov-Krasovskii scheme so that stability is guaranteed during sliding motion. Once the VSC is applied, simulated results are given and it is shown that sliding mode is achieved for any feasible value of the delay and initial conditions.

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