Testing the Controllability of Discrete-Time Linear Systems with Input Constraints

Abstract

This paper gives necessary and sufficient conditions for multiple input discrete-time linear systems to be controllable with input constraints due to saturation and positiveness. These input constraints are very important because they are often encountered in many practical control applications such as optimal drug administration problem, tracer kinetics in medical system, electrically heated oven system, population dynamics, or ecology, etc. Furthermore a simple method to test whether a given system is controllable or not with input constraints is proposed based on the Jordan canonical form by using the elimination method of Gauss and transforming the state and input variables into some particular form. The particular form proposed here contains more informations about the structure of controllable systems with input constraints than that obtained earlier. The results obtained here are expected to become basic frameworks to solve many practical control problems mentioned above.