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This paper presents an input-output simulation approach to controllingmulti-affine systems for linear temporal logic (LTL) specifications, whichconsists of the following steps. First, we partition the state space intorectangles, each of which satisfies atomic LTL propositions. Then, we study thecontrol of multi-affine systems on rectangles including the control of drivingall trajectories starting from a rectangle to exit through a facet and thecontrol of stabilizing the system towards a desired point. With the proposedcontrollers, a finitely abstracted transition system is constructed which isshown to be input-output simulated by the rectangular transition system of themulti-affine system. Since input-output simulation preserves LTL properties,the controller synthesis of the multi-affine system for LTL specifications isachieved by designing a nonblocking supervisor for the abstracted transitionsystem and by continuously implementing the resulting supervisor for theoriginal multi-affine system.

An Input-Output Simulation Approach to Controlling Multi-AffineSystems for Linear Temporal Logic Specifications