Joint order and dependency reduction for LPV state-space models

In the reduction of Linear Parameter-Varying (LPV) models, decreasing model complexity is not only limited to model order reduction (state reduction), but also to the simplification of the dependency of the model on the scheduling variable. This is due to the fact that the concept of minimality is strongly connected to both types of complexities. While order reduction of LPV models has been deeply studied in the literature resulting in the extension of various reduction approaches of the LTI system theory, reduction of the scheduling dependency still remains to be a largely open problem. In this paper, a model reduction method for LPV state-space models is proposed which achieves both state-order and scheduling dependency reduction. The introduced approach is based on an LPV Ho-Kalman algorithm via imposing a sparsity expectation on the extended Hankel matrix of the model to be reduced. This sparsity is realized by an L₁-norm based minimization of a priori selected set of dependencies associated sub-Markov parameters. The performance of the proposed method is demonstrated via a representative simulation example.