An Efficient Algorithm for Optimally Reshaping the TP Model Transformation

The tensor product (TP) model transformation is an emerging technique for the ongoing system analysis and design works of recent years, where its integration with the linear matrix inequalities (LMIs)-based methods can be powerful solution. However, one of the main issues is encountered that the performance of the LMI conditions depends heavily on the tightness of the TP models. This brief proposes an efficient TP model reshaping algorithm toward tightening TP models. A novel index is introduced to quantize the tightness of TP models such that an optimal reshaping can be realized. Besides, a random search following a recursive reshaping strategy is developed, which intensively enhances the efficiency of the reshaping process. The efficiency and effectiveness of the algorithm are demonstrated via a series of numerical simulations.