A predictor feedback control method for time-delay systems using Guass-Legendre integration

Delay is a ubiquitous physical phenomenon in many military and industrial manufacturing processes applications. In real applications control systems with delay, two issues restrict the implementation of the discretized controller: the speed of calculating the controller input and the precision of reconstructing the controller input. The traditional way is to adopt the Newton-Cotes integral formula to estimate the integral formula term to obtain the controller input, which is based on fixed step length and, the reconstructing error is not small enough in several high precision required situations. In this paper, to overcome these two limitations, we proposed to use the Guass-Legendre quadrature formula with three nodes type to reconstruct the control law, and by using the Lyapunov-Krasovskii stability theory, we established conditions to guarantee the stability of the closed-loop system and can obtain the design results in terms of linear matrix inequalities (LMIs). The main contribution of this paper lies in twofold: firstly, a new way of implement the discretized controller consist of integrated terms is suggested, which is potential fast way due to we adopt the three nodes type reconstruction method; Secondly, high precision can be achieved accordingly due to the character of the Guass-Legendre quadrature formula. Simulation results are provided to validate the effectiveness of the proposed methods.