Add to ORKGWe study the problem of feedback control for a class of non-linear hybrid systems characterized by rectangular invariants and multi-affine dynamics, which we call Rectangular Multi-Affine Hybrid Systems. The goal is to find initial states and feedback control strategies so that all trajectories of the closed loop system satisfy arbitrary specifications given as temporal logic formulas over the set of discrete states of the system. Sufficient conditions for solvability are obtained in terms of sets of linear inequalities. If these conditions are satisfied, a control strategy is automatically constructed. The computation consists of polyhedral set operations, construction of B¨uchi automata from linear temporal logic formulas, and searches on...