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

摘要

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.