Delayed Sliding Mode Control Design for Chaotic Systems

This project designs and tests a delayed sliding mode control (DSMC) scheme for chaotic dynamical systems. Chaotic systems react extremely to tiny changes in their starting conditions and show complex, non‑repeating behavior. Because of that, stabilizing them is hard, especially when there are propagation or feedback delays. The method adds a sliding surface that depends on the delay. This lets the controller handle the lag in state feedback while keeping the usual sliding‑mode robustness against disturbances and uncertain parameters. By using Lyapunov‑Krasovskii functionals or other delay‑differential stability tests, the control law is built to guarantee asymptotic stability of the closed‑loop chaotic system. The project also gives step‑by‑step instructions for modeling

chaotic attractors such as the Lorenz or Duffing systems and for implementing the delayed sliding mode controller in a simulation environment. Performance is judged by looking at state trajectories, how quickly the system reaches the sliding manifold, and how much the control input chatter is reduced. Overall, the work provides a practical reference for advanced control design. It helps engineers explore the trade‑offs between allowable delay margins and controller robustness in highly nonlinear systems.

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