Linear and non-linear sliding surfaces in sliding mode control: a review

Purpose The paper surveys the evolution of sliding surface design in variable-structure control with sliding modes. It contrasts linear and nonlinear approaches, outlining how the choice of sliding surface fundamentally shapes closed-loop dynamics. The purpose is to provide researchers and practitioners with a consolidated roadmap to select sliding surfaces that balance simplicity, robustness, and performance for modern control applications. Design/methodology/approach This work systematically reviews classical linear surfaces including proportional, PI/PD, integral, and dynamic extensions and modern nonlinear variants such as terminal, nonsingular terminal, fast terminal, integral terminal, and higher-order surfaces. The methodology involves comparing their convergence properties, robustness to uncertainties, sensitivity to disturbances, and practical implementation challenges such as noise amplification, parameter tuning, and chattering. Findings Linear sliding surfaces deliver predictable exponential convergence and strong disturbance rejection but face limitations under severe uncertainties, noise, and actuator constraints. Nonlinear designs achieve finite-time or prescribed-time convergence, improve robustness against friction and modeling errors, and reduce tracking errors. However, they often introduce greater noise sensitivity and tuning complexity. By contrasting these trade-offs, the survey highlights that no single design is universally optimal, and emphasizes the importance of tailoring surface selection to application-specific demands. Originality/value This survey uniquely bridges the gap between classical linear and emerging nonlinear sliding surface designs by presenting a comparative perspective that emphasizes their trade-offs and complementary strengths. Unlike prior works that focus narrowly on either theory or a specific class of surfaces, this study integrates diverse approaches into a coherent framework. It provides actionable insights for selecting and tailoring sliding surfaces to contemporary control challenges, thereby serving as a practical reference for both academic researchers and practicing engineers.