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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.
The problem of H∞ control for a class of discrete linear systems with state saturation constraints is studied. By introducing a free variable with infinite norm less than or equal to 1, discrete state variables in state saturation constraints are constrained in a convex polytope Based on this, the bounded real lemmas of state-saturated discrete-time linear systems are given and the design algorithm of the state-feedback control law is studied. The conclusions given are expressed as bilinear matrix inequalities, which can be expressed by the proposed iterative linear matrix inequalities Finally, the correctness and validity of the proposed algorithm are verified by numerical examples.