Stabilization of Linear Time-varying Uncertain Delay Systems with Double Triangular Configuration

This paper investigates the feedback stabilization problem of linear time-varying uncertain delay systems using linear memoryless state feedback control. 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 if a system has a particular configuration called a triangular configuration, then the system is stabilizable irrespectively of the given bounds of uncertain variations. In this paper, so far obtained stabilizability conditions are developed into the ones called a double triangular configuration. The objective of this paper is to show that if a system has such an extended configuration, then the system is also stabilizable independently of both the bounds of uncertain parameters and time delays. An illustrative example is presented to verify the effectiveness of the obtained result. Key–Words: Stabilization, Linear systems, Time delay, Uncertain systems, -matrix