状态饱和线性离散系统的H_∞控制

H_∞ synthesis for discrete linear systems with state saturation

研究一类具有状态饱和约束的离散线性系统的H∞控制问题.通过引入一个无穷范数小于等于1的自由变量,将状态饱和约束下的离散线性系统状态变量约束在一个凸多面体内.在此基础上,给出了状态饱和离散线性系统的有界实引理,并研究了状态反馈控制律设计算法.所给出的结论表示为双线性矩阵不等式,可通过所提出的迭代线性矩阵不等式算法求解.最后通过数值例子验证了所提出算法的正确性和有效性.

This paper studies the H∞ synthesis for discrete linear systems with state saturation nonlinearity.By introducing a free matrix whose infinity normis less than or equal to 1,the state under saturation constraint is confined in a convex hull.Based on this,a bounded real lemma for discrete linear systems with state saturation is obtained in terms of matrix inequalities which can be solved by using the presented iterative linear matrix inequality algorithm.The synthesis problem is also solved and an explicit expression for the desired state feedback control law is given.A numerical example shows the effectiveness and correctness of the presented method.