CONTROL OF A COLLECTION OF LINEAR-SYSTEMS BY LINEAR STATE-FEEDBACK CONTROL

Controlling a collection of linear multiple input systems with a singl e linear state feedback controller is considered. A straightforward nu merical procedure, which is based on the minimization of a weighted su m of the quadratic performance indices of the systems is presented. In this method the performance of the closed loop systems, rather than s imultaneous 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 stabili zing each member of the collection of systems. Furthermore, through th e choice of the quadratic performance index, it is possible to limit t he size of the feedback controller by changing a single user specified parameter and thus ensure that the control action is not excessive. T wo examples are used to illustrate and to test the procedure.