Robust Stability of Periodic Systems with Memory: New Formulations, Analysis and Design Results

In this paper, the general formulation of periodically time-varying state-feedback controllers with memory is considered for the first time. New analysis and synthesis conditions for robust stability are proposed. The flexibility of these new results allows the user to freely add degrees-of-freedom to the control law which appears to effectively reduce the conservatism of the synthesis condition and to increase the stability domain of the closed-loop system in the presence of uncertainties. Furthermore, it is shown that for a particular structure of controllers a more efficient version of the design theorem can be derived by enriching the matrix of slack-variables.