Delay-independent Stability for Systems with Single Output Delays

Abstract

Influence of delays cannot be negligible in many control systems, since delays often times cause instability as found in engineering, biology, process control, and economics. A careful controller design is therefore critical in order to assure that the controlled system performs properly and remains stable despite the existence of delay. When the delay is unknown, and/or cannot be measured, then controlling a system becomes very difficult: How can we control the system without knowing the delay in the control loop? To circumvent this, we developed an algebraic approach to design controllers that can control the system “no matter how large/small the delays are.” That is, with our design the controller works regardless of delays. Having solved this difficult problem, we can use its strengths to stabilize various dynamical systems in which presence of delays are inevitable. We test our designed controllers on benchmark problems with simulations to validate the theoretical results.