On the effects of redundant control inputs in discrete-time systems

This paper considers the effects of the redundant control inputs in discrete-time systems. A necessary and sufficient condition for the strict decrease of the quadratic performance index with input extension is introduced. For the non-strict decrease cases, the initial state set is determined by using simplictic matrix eigenvectors and generalized eigenvectors. The guaranteed cost problem is also solved for uncertain systems with input extension. An optimizing iterative algorithm is presented to choose the input matrix columns for a better performance index. An example is given to illustrate the results.