Time-varying low gain feedback for linear systems with unknown input delay

Abstract

In this paper, the traditional low gain feedback design with a time-invariant feedback parameter is generalized to time-varying parameter design for linear systems with delayed input. For an unknown delay with a known upper bound, a time-varying low gain feedback law, constructed by using the parametric Lyapunov equation based approach, globally regulates a system with all open loop poles at the origin as long as the time-varying low gain parameter has a continuous second derivative and approaches a sufficiently small constant with its derivative approaching zero as time goes to infinity. Improvement of the closed-loop performance is addressed in a convergence rate analysis and then observed in simulation compared with the traditional constant parameter low gain design.