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研究了状态饱和奇异离散线性系统的稳定性分析与状态反馈控制律综合问题.通过引入无穷范数小于等于1的自由矩阵,将状态饱和奇异离散线性系统的状态变量约束在一个顶点与自由矩阵相关的凸多面体内,从而将状态饱和非线性奇异离散系统的稳定性分析问题转换成具有凸多面体不确定参数的奇异离散线性系统的鲁棒稳定性分析问题,引入自由矩阵来描述奇异离散系统代数子系统变量与差分子系统变量的代数约束关系,给出了状态饱和奇异离散线性系统的正则、因果和渐近稳定的新判据,并给出了相应的状态反馈控制律综合算法.稳定性判据与控制律设计算法以矩阵不等式形式给出,可以使用所提出的迭代线性矩阵不等式算法求解.数值例子验证了算法的有效性与正确性.
The stability analysis and the state feedback control law synthesis problem for state-saturated singular discrete linear systems are studied. By introducing a free matrix with infinite norm less than or equal to 1, the state variables of state-saturated singular discrete linear systems are constrained to one vertex associated with the free matrix To solve the problem of robust stability of singular discrete linear systems with convex polytopic uncertainties. A free matrix is introduced to describe the singular discrete system algebras The algebraic constraints of the system variables and the differential system variables, the new criterion for the regular, causal and asymptotic stability of the state-space singular discrete linear systems is given and the corresponding state feedback control law synthesis algorithm is given. According to the algorithm of control law design given in the form of matrix inequality, we can use the proposed iterative linear matrix inequality algorithm to solve the numerical examples verify the validity and correctness of the algorithm.