状态饱和奇异离散线性系统的稳定性分析与控制律综合

Stability Analysis and Controller Synthesis for Singular Discrete Linear Systems with State Saturation

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 problem of stability analysis and state feedback controller synthesis for singular discrete linear systems with state saturation is studied. By introducing a free matrix whose infinity norm is less than or equal to 1, the state variables under saturation constraint are confined in a convex hull whose vertexes are associated with this free matrix. Based on this, the original stability problem of singular discrete systems with state saturation nonlinearity is transformed into the robust stability analysis problem of linear singular discrete systems with polytopic type uncertain parameters. With the introduction of a free matrix to draw the relationship between algebraic subsystem variables and difference subsystem variables, a sufficient criterion for discrete linear singular systems with state saturation to be regular, causal and asymptotically stable, is obtained in terms of matrix inequalities. The corresponding state feedback control law synthesis algorithm is also given. The obtained stability criterion and controller design algorithm are given in terms of matrix inequalities that can be solved using the presented iterative linear matrix inequality algorithm. Numerical examples are used to show that the presented method is applicable and effective.