Virtual State Coupled Sliding Mode Control: An Energy Exchange Approach with Tunable Performance Trade-Off

Traditional sliding mode control (SMC) lacks an active mechanism for redistributing energy among state channels during transient convergence, resulting in a rigid trade-off between response speed, overshoot suppression, and energy efficiency. This paper proposes a virtual state coupled SMC method that introduces a dynamic virtual state with bilinear product coupling x1x2 into the sliding surface. Unlike conventional virtual states that serve as static linear combinations or observer-based estimates, the proposed virtual state evolves dynamically and establishes an active energy exchange channel between the real and virtual state dynamics. Linearization and Lyapunov-based analyses prove local asymptotic stability of the closed-loop system. The coupling strength γ is shown to be decoupled from the linearized local eigenvalues and thus governs the energy-performance trade-off independently, while the condition c>γ/4 guarantees a non-vanishing domain of attraction. Simulations demonstrate that the proposed method achieves up to 53.2% control energy reduction under disturbance-free conditions compared with conventional SMC. Under persistent high-frequency disturbances, increasing γ reduces oscillations by 54.2% at a controllable energy cost of 45.7%. Systematic parameter selection guidelines are provided, and Monte Carlo simulations (500 trials, ±30% parameter perturbations) confirm 100% convergence. The proposed method offers an independently adjustable energy-performance trade-off mechanism suitable for sensor-based motion systems with stringent transient and energy requirements.