Control-Parameter-Space Classification for Delay-Independent-Stability of Linear Time-Invariant Time-Delay Systems; Theory and Experiments

Reading the instantaneous reaction (states) of dynamic systems subjected to internal/external inputs is almost impossible in practice. To overcome the problem of this loss of information, in theory, it is preferred to include the information of the dynamic states of the system within its mathematical model.;Even for linear time-invariant (LTI) systems, control design in the presence of delays can be challenging, especially within a non conservative framework. Frequency domain technique (FDT) is one promising direction for obtaining non-conservative results as demonstrated for analysis and synthesis problems of LTI systems.;Within this dissertation, a purely algebraic approach is developed for designing controllers for regulation purposes of the general class of linear time-invariant (LTI) systems with uncertain delays. The results are new and address the major issue of extending the DIS control design to increased number of discrete delays. This is achieved mainly by procedures based on algebraic tools which allow designing controllers that can stabilize such systems regardless of how large/small the delays are.