Parametrization of completeness in symbolic abstraction of bounded input linear systems

A good state-time quantized symbolic abstraction of an already input quantized control system would satisfy three conditions: proximity, soundness and completeness. But instability of systems, whose inputs are bounded and quantized, is an impediment to constructing fully complete state-time quantized symbolic models, even using supervisory feedback. In this paper, we come up with a way of parametrization of completeness of the symbolic model through the quintessential notion of “Trimmed-Input Approximate Bisimulation” which is introduced in the paper. The amount of completeness is reflected by a parameter called “trimming” of the set of input trajectories. We subsequently discuss a procedure of constructing state-time quantized symbolic models which are near-complete in addition to being sound and proximate with respect to the time quantized models.