Stabilization of Linear Uncertain Delay Systems with Antisymmetric Stepwise Configurations

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 might vary with time in an arbitrarily large range. In such a situation, the locations of uncertain elements in the system matrices play an important role. Wei introduced the concept of antisymmetric stepwise configuration (ASC) and proved that it is a necessary and sufficient condition for linear uncertain systems to be quadratically stabilizable using linear state feedback control to have this configuration. However, his method is inapplicable to systems that contain delays in the state variables. On the other hand, Amemiya developed conditions for the stabilization of linear uncertain systems with state delays using linear memoryless state feedback control. This paper presents development of the conditions of this problem that have been obtained to date. Fundamentally, it is proved that having an ASC is also a sufficient condition for the stabilization of linear uncertain delay systems. For systems satisfying the stabilizability conditions, a simple control design procedure is also provided and illustrated by an example.