This paper considers effects of redundant control inputs on System performance. A necessary and sufficient condition for 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 Hamilton matrix eigenvectors and generalized eigenvectors. The H-2 optimal control problem is similarly studied on the basis of state feedback and dynamic output feedback controllers. Both linear matrix inequality (LMI) and Riccati equation based methods are established. The guaranteed cost problem is also solved for uncertain systems with input extension. An iterative optimization algorithm is presented, for choosing the input matrix columns for a better performance index. A satellite launch vehicle (SLV) system is used to illustrate the results. (C) 2012 Elsevier Ltd. All rights reserved.