Minimum Energy Control and Reachability of Continuous-Time Linear Systems with Rectangular Inputs

In the paper a reachability property of continuous-time linear systems with rectangular type inputs vector is addressed. Necessary and sufficient conditions for the existence of that type of input signals that steer the system from zero initial conditions to desired final state in assumed time are derived and proved. The computation method of the input signals vector set that are the solution to the problem is presented. Next, a minimum energy control problem is considered. Using an integral control performance index the minimum energy input vector is chosen from the set of consistent inputs. The considerations are illustrated by a numerical example of electrical circuit with pulse wave voltage sources, where the input signals that minimise assumed performance index are computed and applied to steer the electrical circuit to desired final state in given time.