$H_{\infty}$ Control for Networked Predictive Control Systems Based on the Switched Lyapunov Function Method

Abstract

This paper investigates the problem of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for a class of networked control systems (NCSs) with time-varying delay in both forward and backward channels. Combined with the switched Lyapunov function technique, an improved predictive controller design strategy is proposed to compensate for the delay and data dropout to achieve the desired control performance. Based on these methods, the controllers can be designed to guarantee that the closed-loop system is asymptotically stable with an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm bound in terms of nonlinear matrix inequalities. An iterative algorithm is presented to solve these nonlinear matrix inequalities to obtain a suboptimal minimum disturbance attenuation level. Numerical simulations and a practical experiment are given to illustrate the effectiveness of the proposed method.