Control of a collection of linear systems by linear state feedback control

Abstract

Controlling a collection of linear multiple input systems with a single linear state feedback controller is considered. A straightforward numerical procedure, which is based on the minimization of a weighted sum of the quadratic performance indices of the systems is presented. In this method the performance of the closed loop systems, rather than simultaneous stabilization, is the primary consideration. The proposed procedure is computationally efficient and since only an unconstrained minimization problem must be solved, it is also simple to implement. The resulting controllers are found to be effective at rapidly stabilizing each member of the collection of systems. Furthermore, through the choice of the quadratic performance index, it is possible to limit the size of the feedback controller by changing a single user specified parameter and thus ensure that the control action is not excessive. Two examples are used to illustrate and to test the procedure.