OPTIMAL STATE-FEEDBACK CONTROL WITH A PRESCRIBED CONTRACTION PROPERTY

In this paper, we consider time-varying state feedback control of sing le-input linear time-invariant discrete-time systems. The approach tha t we propose is based on a contraction property that was introduced in a previous paper. All time-varying controllers that yield the contrac tion property are derived. It is seen that the state feedback vector b ecomes m-periodic, where the integer m is a user parameter related to the obtained contraction property. From the class of control laws that yield the contraction property, we determine the controller which min imizes a linear quadratic criterion. Results that are useful for tunin g one of the user parameters are presented. Numerical examples which c ompare the methods are also included.