Stabilization of linear uncertain delay systems irrespective of bounds of uncertain variations

This paper investigates the problem of designing a linear memoryless state feedback control to stabilize a class of linear uncertain systems with state delays. Each uncertain parameter and each delay under consideration may take arbitrarily large values. In such a situation, the locations of uncertain entries in the system matrices play an important role. It has been shown that it is a necessary and sufficient condition for the stabilization of time-varying or time-invariant uncertain systems without delays to have a particular geometric configuration called an ASC or a GASC, respectively. However, those results are inapplicable to systems that contain delays in the state variables. The objective of this paper is to show that if time-varying uncertain systems with time-varying delays or time-invariant uncertain systems with time-invariant delays have an ASC or a GASC, respectively, then the systems are stabilizable no matter how large the bounds of delays and uncertain parameters may be. However, we restrict our attentions to 3-dimensional systems for simplicity. The results shown here imply that the stabilizability conditions are not deteriorated by the existence of time delays.