Higher-Order Frozen-Time Models of Linear Time-Varying Systems

The paper deals with the construction of generalized frozen-time (FT) models-for linear time-varying continuous-time systems. The generalized FT models are higher-order models generated from a given n-dimensional state model by applying a stable differential operator to the state equation. This results in FT models whose coefficients depend on the derivatives of the time-varying system coefficient matrices. The accuracy of the higher-order FT models over local time intervals is investigated in terms of truncated Taylor series. In the last part of the paper, the application of the higher-order FT models to state feedback control is considered.