A Delay Independent Output Feedback Law for Linear Systems with Time-Varying Input Delay

Abstract

It is well-known that a delay-dependent or delay-independent truncated predictor feedback law stabilizes a general linear system in the presence of a certain amount of input delay. Results also exist on estimating the maximum delay bound that guarantees stability. In the face of time-varying or unknown delay, delay independent feedback laws are preferable over delay-dependent feedback laws as the former provide robustness to uncertainties in the delay. In light of few results on the construction of delay-independent output feedback laws for general linear systems with input delay, we present in this paper a delay-independent observer based output feedback law that stabilizes the system. Our design is based on the truncated predictor feedback design. We establish an estimate of the maximum allowable delay bound through Razumikhin-type stability analysis. The delay bound result reveals the capability of the proposed output feedback law in handling an arbitrarily large input delay in linear systems with all open loop poles at the origin or in the open left-half plane. Compared with that of the delay-dependent output feedback laws in the literature, this stabilization result for systems with all poles at the origin or in the open left half plane is not sacrificed by the absence of the knowledge of the delay.