Prediction-based control of multi-input linear systems subject to distinct unknown delays.

The paper is concerned with the stability of linear time-invariant (LTI) systems with distinct multi-input unknown delays. Our method is based on transport partial differential equations (PDEs) representation of the multi-input delays and infinite-dimensional backstepping transformation. By introducing the new Lyapunov–Krasovskii functional, exponential stabilization of the closed-loop system is achieved, in which fixed constant horizon prediction-based controllers are introduced to robustly compensate for the different delays. There are two control designs proposed: single-constant and multi-constant horizon prediction-based control design. For the latter, we introduce special infinite-dimensional backstepping transformation, backstepping-forwarding transformation, to offset delays from small to large. In particular, constants selection are required to be within a narrow enough range. At last, to illustrate the validity of the proposed results, a numerical example is provided. [ABSTRACT FROM AUTHOR]