基于LMI的范数有界不确定仿射离散时滞系统的鲁棒控制

LMI-based robust control of norm-bounded uncertain affined discrete systems with state delay

针对一类带有时滞的范数有界不确定仿射离散系统,为了研究其相应闭环系统鲁棒稳定性,采用构造相应二次Lyapunov函数的方法,结合线性矩阵不等式(LMI)技术,设计出系统稳定的状态反馈鲁棒控制器.获得了该仿射系统渐进稳定的一个充分条件,从而表明该仿射系统渐进稳定性是可实现的.线性矩阵不等式可以利用已有的凸优化技术求解.最后通过仿真算例验证了该方法的正确性和有效性.

Focusing on a class of norm-bounded uncertain affine discrete systems with state delay, in or- der to guarantee the asymptotic stability of the system, a state feedback controller is proposed. This controller is expressed in terms of linear matrix inequalities（LMIs） based on the discrete-type quadratic Lyapunov function. A sufficient condition for this kind of affine systems is constructed to prove that the asymptotic stability of the system can be realized. The solution of the LMIs can be solved easily by ex- isting efficient convex optimization techniques. A numerical example is given to illustrate the effective- ness of the proposed theoretical results.