Truncated predictor feedback stabilization of polynomially unstable linear systems with multiple time-varying input delays

This technical note is concerned with stabilization of polynomially unstable linear systems with multiple time-varying input delays. A truncated predictor feedback (TPF), which is obtained by truncating the distributed terms in the traditional predictor feedback, is proposed. The proposed TPF is a linear static partial state feedback with a time-varying feedback gain that is constructed from the steady solution to a class of parametric Lyapunov differential equations. Under the assumption that the open-loop system is only polynomially unstable and is uniformly controllable, it is shown that, for sufficiently small value of the design parameter, the resulting closed-loop system is exponentially stable no matter how large the time-varying delays are as long as they are bounded. Simulation demonstrates these theoretical results.