一类2-D系统的鲁棒稳定性分析

研究了2-D系统第二类Fornasini-Machesini模型的稳定性问题,以线性矩阵不等式的形式给出了一类不确定2-D系统的鲁棒渐近稳定条件.在定义了稳定界的基础上,提出了稳定界的求取方法.进而得出了该类系统稳定状态反馈控制律的存在条件和设计方法,利用一组线性矩阵不等式的可行解给出了反馈控制律的参数化表示,理论上证明了该方法设计的控制器使得闭环系统对于所有允许的不确定性均稳定.系统的稳定界和反馈控制器可以通过求解一类线性矩阵不定式约束的凸优化问题得到.

Analysis of robust stability for 2-D systems

The robust stability for the second Fornasini-Marchesini model of 2-D systems was studied by using linear matrix inequality (LMI) technology. The robust asymptotical stability criteria for a class of uncertain 2-D systems were presented in the form of LMI. Based on the definition of the robust stable bounds, the way to determine the robust stable bound was proposed. Then, the existence condition and design procedure of state feedback controller for this class of systems was given. The parameterized representation of feedback controller was provided in terms of the feasible solutions to a certain LMI. It was proved that the controller designed by using this approach can render the closed-loop system to be asymptotical stability for all admissible uncertainties. The robust stable bound and the state feedback controller can be obtained by solving a class of convex optimization problems with LMI constraint.