Testing the constrained controllability of discrete-time linear systems

Necessary and sufficient conditions are given for multiple input discrete-time linear systems to be controllable where the inputs are constrained to be greater than some negative values. Furthermore a simple method to test the controllability with input constraints is proposed by using the Jordan canonical form and constructing some particular form of input matrices based on the elimination method of Gauss. The particular forms proposed here suggest perspective structures of controllable systems with input constraints and are useful in dealing with fundamental control problems.