随机线性重复过程的鲁棒H_∞模型降阶

Robust H_∞ Model Reduction of Stochastic Repetitive Processes

研究随机线性重复过程的鲁棒H∞模型降阶问题,针对一个给定的随机线性重复过程,为构造降阶模型使误差随机线性重复过程均方渐进稳定且具有H∞性能约束,提出建立随机线性重复过程的H∞性能准则,利用投影引理求解模型降阶问题。将容许的降阶模型存在的充分条件表达成具有逆约束的线性矩阵不等式(LMI)形式。所得的条件不是严格的线性矩阵,可利用锥补线性化的方法转化为受线性矩阵不等式约束的非线性最小问题要标准软件上进行仿真。仿真结果证实设计方法的有效性。

The paper investigates the problem of H∞ model reduction for a class of stochastic linear repetitive processes which are a distinct class of 2D linear systems with theoretic and applications interest.For a given mean-square asymptotically stable stochastic repetitive processes,the purpose is to construct reduced-order repetitive processes,which approximate the original repetitive processes well in an H∞ norm sense.The H∞ gain criterion is first established for stochastic linear repetitive processes,and the corresponding model reduction problem is solved by using projection lemma,with sufficient conditions obtained for the existence of admissible reduced-order solutions.Since these obtained conditions are not expressed as strict linear matrix inequalities（LMIs）,the cone complementary linearization（CCL） method is exploited to cast them into sequential minimization problems subjected to LMIs constraints,which can be readily solved by using standard numerical software.The efficiencies of the theories scheme are demonstrated via a numerical example.