不确定线性2-D离散系统的鲁棒滑模控制

Robust sliding mode control for a class of uncertain linear 2-D discrete-time systems

针对不确定线性离散二维(2-D)系统,研究了其鲁棒稳定性、鲁棒镇定和鲁棒滑模控制问题.基于线性矩阵不等式的方法推导了该系统鲁棒渐近稳定的充分条件,并给出了系统状态反馈镇定器和理想滑动模态存在的充分条件.改进了离散时间滑模控制系统的趋近律方法,使得状态能够到达滑模面上产生理想的滑动模态,并将其推广应用到2-D离散系统中,综合了一类滑模控制器保证闭环系统鲁棒渐近稳定.仿真实例证实了该设计方法的有效性.

For a class of uncertain linear twodimensional（2-D） discrete-time systems,the problems of robust stability analysis,state feedback robust stabilization and robust sliding mode control is concerned.A sufficient condition is proposed for robust asymptotic stability of the autonomic system in terms of linear matrix inequality（LMI）.Based on that condition,some sufficient conditions are also developed for the existence of stabilization controller and ideal sliding mode.Moreover,the reaching law method used for one-dimensional（1-D） discrete-time systems is further extended and improved to investigate the sliding mode controller（SMC） design for 2-D discrete-time system.A SMC is synthesized by using the extended reaching law method,which guarantees the closed-loop system robust and asymptotically stable.A numerical example illustrates the effectiveness of the proposed design scheme.