Lyapunov-Krasovskii functionals for predictor feedback control of linear systems with multiple input delays

This paper is concerned with the Lyapunov-Krasovskii functional construction of linear control systems with multiple input delays. By transforming the predictor feedback control systems into a delay-free linear system with external inputs, a Lyapunov-Krasovskii functional is constructed in terms of a set of linear matrix inequalities (LMIs). It is shown that the solvability of this set of LMIs is equivalent to the asymptotic stability of the delay-free linear system induced from the predictor feedback control system. The proposed Lyapunov-Krasovskii functional is also found to be an ISS Lyapunov-Krasovskii functional for the predictor feedback control systems. An example is worked out to validate the effectiveness of the proposed method.