For MIMO nonlinear systems with vector relative degree, box constraints on outputs yield mutually compatible control barrier function constraints, and the quadratic-programming safety filter is Lipschitz and closed-form under a Gram-matrix cost.
Data-driven safety filters: Hamilton-Jacobi reachability, control barrier functions, and predictive methods for uncertain systems,
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Compatibility of Multiple Control Barrier Functions for Constrained Nonlinear Systems
For MIMO nonlinear systems with vector relative degree, box constraints on outputs yield mutually compatible control barrier function constraints, and the quadratic-programming safety filter is Lipschitz and closed-form under a Gram-matrix cost.