Sliding-Mode Control for Perturbed MIMO Systems With Time-Synchronized Convergence

This article introduces a novel approach called terminal sliding-mode control for achieving time-synchronized convergence in multi-input–multi-output (MIMO) systems under disturbances. To enhance controller design, the systems are categorized into two groups: 1) input-dimension-dominant and 2) state-dimension-dominant, based on signal dimensions and their potential for achieving thorough time-synchronized convergence. We explore sufficient Lyapunov conditions using terminal sliding-mode designs and develop adaptive controllers for the input-dimension-dominant case. To handle perturbations, we design a multivariable disturbance observer with a super-twisting structure, which is integrated into the controller. By utilizing the sliding-mode technique and the disturbance observer, the proposed controller ensures simultaneous convergence of all output dimensions. In the state-dimension-dominant case, where a full-rank system matrix is absent, only specific output elements converge to equilibrium simultaneously. We conduct comparative simulations on a practical system to highlight the effectiveness of our proposed method for the input-dimension-dominant case. Statistical results reveal the benefits of shorter output trajectories and reduced energy consumption. For the state-dimension-dominant case, we present numerical examples to validate the semi-time-synchronized property.