On Some Structures of Stabilizing Control Laws for Linear and Time-Invariant Systems with Bounded Point Delays and Unmeasurable State

The output-feedback stabilization is considered by linear dynamic controllers of (open-loop) stabilizable and detectable time-invariant plants involving a finite set of bounded internal point delays. Two controllers involving, respectively, point and distributed delays are studied as well as their extension to the use of a feedback signal consisting of convolutions of the system output and controller state with an appropriately chosen linearly independent set of functions. It is concluded that an increase in the order of the controller dynamics can be used as an alternative stabilization technique to the use of delays in the controller.