Grid-Free Constraints for Parameter-Dependent Generalized Gramians via Full Block S-Procedure
This paper shows how the computational effort required for the computation of parameter-dependent generalized Gramians (PDGGs) for linear parameter-varying (LPV) systems with more than two scheduling parameters can be significantly reduced by using a grid-free approach. This approach is applicable to LPV systems that can be expressed as linear fractional representations. The constraints for generalized Gramians are reformulated according to the full block S-procedure (FBSP) lemma, which eliminates the need for gridding by imposing a DG-scale structure on the multipliers. A case study on numerical examples illustrates the benefits of PDGGs in the balanced truncation method and shows a considerable improvement in computation time when there are more than two scheduling parameters. Moreover, the results suggest that the conservatism due to using DG-scalings does not affect the quality of the reduced models.