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.
Towards a framework for realizable safety critical control through active set invariance,
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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.