A delay-independent output feedback law for discrete-time linear systems with bounded unknown input delay

Bounded input delay frequently arises in discrete-time linear systems. The standard predictor feedback design requires the exact knowledge of the delay. Such a requirement on the availability of the delay knowledge poses challenges in the design of robust control laws when only the knowledge of an upper bound of the delay is known. We propose such a design in this article. Based on the delay-independent truncated predictor state feedback design, an observer-based output feedback law is constructed that does not contain any explicit information of the delay. For a general, possibly exponentially unstable, discrete-time linear system, the proposed output feedback law stabilizes the system as long as the delay does not exceed a certain amount. For the special case of systems with all the open-loop poles on or inside the unit circle, a low gain feedback design is presented. This low gain design allows us to establish that, when all the open-loop poles of a system are at z = 1 or inside the unit circle, stabilization can be achieved for an arbitrarily large bounded delay as long as the value of the low gain parameter is chosen small enough.

Automated summary

In this article, a design is proposed to stabilize general, possibly exponentially unstable, discrete-time linear systems by constructing an observer-based output feedback law, as long as the delay does not exceed a certain amount. For systems with all the open-loop poles on or inside the unit circle, a low gain feedback design is presented, which allows stabilization to be achieved for an arbitrarily large bounded delay when the low gain parameter is chosen small enough.