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This chapter presents a Lyapunov-based analysis of a difference equation utilizing a minima-based law for discrete-time sliding mode control. We derive Lyapunov stability conditions and demonstrate the finite-time input-to-state stability of perturbed discrete-time systems. The analysis shows that the proposed method strikes a balance between Gao’s and Utkin’s reaching laws, effectively mitigating the key limitations of each–namely, chattering in Gao’s approach and overly large control actions in Utkin’s. The minima-based difference equation is applied to the design of discrete-time sliding mode control for both first- and second-order perturbed systems. Simulations are provided to compare the proposed method with existing discrete sliding mode control (DSMC) approaches, highlighting its superior performance.

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A Lyapunov Characterization of Difference Equation with Minima Based Discrete Sliding Mode Control

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  • 发表日期：

    2026年

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  • Shyam Kamal,
  • Parijat Prasun

摘要

This chapter presents a Lyapunov-based analysis of a difference equation utilizing a minima-based law for discrete-time sliding mode control. We derive Lyapunov stability conditions and demonstrate the finite-time input-to-state stability of perturbed discrete-time systems. The analysis shows that the proposed method strikes a balance between Gao’s and Utkin’s reaching laws, effectively mitigating the key limitations of each–namely, chattering in Gao’s approach and overly large control actions in Utkin’s. The minima-based difference equation is applied to the design of discrete-time sliding mode control for both first- and second-order perturbed systems. Simulations are provided to compare the proposed method with existing discrete sliding mode control (DSMC) approaches, highlighting its superior performance.