The next task is robustness
When designing a robust closed-loop control, we take system uncertainties into consideration, i.e. specify the nominal values of certain system parameters and the domain of changes around these values. The controller must be designed so as to ensure optimal control at nominal parameter values but prevent control failure (instability) if parameters change, while maintaining an acceptable level of quality.
Within the boundaries of design circumstances, a robust system only differs from optimal operation to an anticipated, insignificant extent. The design process is carried out on the basis of the Hardy spaces calculating measures.
Generally, there is no perfectly optimal way to fulfil these requirements, so systems are designed to stay in the multidimensional domain of small changes in quality characteristics.
Due to their complexity, designing such systems is particularly difficult and calls for the utilisation of the tools of modern control theory, including control paths transformed into various spaces. System engineers try to describe the diverse shapes of robustness domains with spaces which show these border shapes of robustness in a way that is calculable and detectable.