Robust input redundancy for uncertain systems

For input redundant linear systems, it is possible to construct distinct inputs producing identical outputs, from the same initial state. Thus selecting an output does not determine uniquely the input, i.e., there exist degrees of freedom related to the choice of inputs to generate a given output. These degrees of freedom can be used to enhance the system performances without altering the output. However their determination might depend on system parameters. When some of them are not known or uncertain, it may be difficult or impossible to design distinct inputs leading to the same output. Considering uncertainties in linear systems, this paper determines if such degrees of freedom exist independently from the uncertain parameters and, in this case, provides a methodology to compute these inputs. This corresponds to the new concept of robust input redundancy, which is defined and characterized in this paper.