2-D系统的稳定性问题  

STABILITY OF 2-D STATE-SPACE SYSTEMS

作　　者：赵胜民[1] 唐万生[1] 李光泉[1] 

机构地区：[1]天津大学系统工程研究所,天津300072

出　　处：《自动化学报》2002年第4期620-624,共5页Acta Automatica Sinica

基　　金：天津市自然科学基金 ( 96 36 0 9511)资助

摘　　要：以线性矩阵不等式为工具 ,研究有关 2 - D系统第二类 Fornasini- Marchesini模型的稳定性的问题 .首先提出了该类系统的一种 Lyapunov不等式 ,由此给出了该类系统渐近稳定的新的判别条件 .其次 ,给出了该类系统能稳定化的充分条件和反馈矩阵的求法 .最后 ,提出了一种求该类系统的稳定性裕度下界的方法 ,并指出了利用该方法得到的稳定性裕度的下界大于原有文献中给出的下界 .The stability problems for the second Fornasini-Marchesini model of 2-D systems are investigated by using linear matrix inequality. First, a kind of 2-D Lyapunov inequality is proposed, and some new criteria for asymptotical stability of the systems are given. Secondly, the sufficient conditions for stabilization of the systems are derived and the algorithm for determining the feedback matrix is presented, too. Finally, a new algorithm for computing a lower bound for the stability margin of the systems is proposed. It is shown that the lower bound obtained by this algorithm is less conservative than the existing ones.

关 键 词：2-D系统 稳定性问题 渐近稳定性 能稳定性裕度 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]