Uncertain frequency domain estimates for LTV discrete-time systems

Although upper bound estimation or the worst case gain analysis are well known methods for linear time invariant (LTI) systems, they cannot be applied directly for linear time varying systems (LTV). The main aim of the paper is to extend the methodology to the LTV case. Our approach base on approximated magnitude-frequency response using SVD-DFT method for LTV systems. The upper bound is estimated using geometrical approach for complex numbers of the approximated magnitude-frequency response. Our considerations begins from description of discrete-time LTV state space model with additive uncertainty and equivalent operators notation with additive perturbation of the system operator. Further the relationship for system additive perturbation operator is proved as well as it is shown how the results can be employed for estimation of the upper bound on magnitude diagram. Theoretical considerations are complemented by numerical example - upper bound analysis for uncertain variable structure system.