Optimal State Feedback Control with a Prescribed Contraction Property

Abstract In this paper time-varying state feedback control of single input linear time-invariant discrete-time systems is considered. The proposed approach is based on a contraction property that was introduced in a previous paper. All time-varying controllers that yield the contraction property are derived. From the class of control laws that yield the contraction property, the controller which minimises a linear quadratic criterion is determined. Results that are useful for tuning one of the user parameter are presented. Numerical examples which compare the methods are also included.