Grid-Free Model Order Reduction for Linear Parameter-Varying Systems via Full Block S-Procedure

This paper shows how the computational effort required for the balanced truncation of linear parameter-varying (LPV) systems with more than one scheduling parameter 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 full block S-procedure (FBSP) is used to calculate generalized Gramians, and the need for gridding is eliminated by imposing a DG-scale structure on the multipliers. A numerical study on a chained multiple mass-spring-damper system with parameter-dependent spring constants illustrates considerable improvement in computation time when there is more than one scheduling parameter. Moreover, the results suggest that the conservatism due to using DG-scales does not affect the quality of the reduced models.