中文摘要：

为消除未知情况下外部干扰和测量噪声对控制系统性能的不利影响，以一类参数不确定性体现为范数有界形式的离散广义分段仿射系统为模型，研究具有H∞性能指标渐近稳定弹性滤波器的设计问题。通过采用广义分段仿射Lyapunov函数、投影定理以及几个基本引理，提出了对于由所设计弹性滤波器构成的滤波误差动态系统满足鲁棒H∞性能指标的反馈控制器设计方法。通过求解一组包含参变量的LMIs，可以得到保证广义分段仿射系统具有H∞性能的反馈控制器增益和渐近稳定弹性滤波器的待定系统矩阵，仿真结果证明了所提设计方法的有效性。

英文摘要：

This paper investigates the robust admissibility analysis and resilient filter controller synthesis for a class of discrete-time piecewise affine singular systems with asymptotic stability which possesses H∞performance is considered in this paper, in order to eliminate the adverse effects of external disturbances and measurement noise of control system performance. By using the piecewise-affine singular Lyapunov functions combined with Projection lemma and some basic lemmas, an approach of designing robust H∞ feedback controller is given, the conclusions ensure resilient filtering error dynamic system possessing H∞ performance. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by scalar variables. The feedback controller gain and resilient filter system matrix can ensure the stability of systems and guarantee the H∞ performance of the piecewise-affine singular systems. Finally, the practicability of the proposed methodologies is confirmed via some simulation examples.