Model Order Reduction of Switched Linear Systems with constrained switching
Model Order Reduction of Switched Linear Systems with constrained switching
复制标题
具有约束切换的切换线性系统的模型降阶
DOI：
10.1007/978-3-030-21013-7_3
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Gosea I.V., Pontes Duff
中科院分区：
文献类型：
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作者：
Gosea I.V., Pontes Duff
在这项工作中，我们提出了一个平衡的截断过程减少大规模切换线性系统（SLS）的特点是约束切换的情况。为此，我们引入新的广义可达性和可观测性Gramian，相关的约束切换序列，满足耦合李雅普诺夫方程。主要目标是利用新引入的Gramian矩阵来发展一种平衡型的模型降阶（莫尔）方法 的约束切换SLS。通过遵循线性时不变（LTI）系统的经典方案，与小奇异值相关的子空间可以被截断，从而得到降阶的SLS。最后，几个数值例子证明了所提出的近似的效率。
In this work, we propose a balanced truncation procedure for the reduction of large-scale switched linear systems (SLSs) which are characterized by constrained switching scenarios. To this aim, we introduce new generalized reachability and observability Gramians, related to the constrained switched sequences, which satisfy coupled Lyapunov equations. The main goal is to make use of the newly introduced Gramian matrices to develop a balancing-type procedure for model order reduction (MOR) of constrained switching SLSs. By following the classical scheme for linear time-invariant (LTI) systems, the subspaces that are related to small singular values can be truncated leading to reduced order SLSs. Finally, the efficiency of the proposed approximation is demonstrated by several numerical examples.