Switching LTI Models via Haar Transform for Non-Stationary Dynamic Systems Modeling

This paper presents a new technique for modeling Linear Parameter Varying (LPV) and quasi-LPV systems, which can be used to represent a wide range of nonlinear dynamic systems, by a set of switched Linear Time Invariant (LTI) models. The switched LPV model is obtained by minimizing, for frozen parameter values, the error between its dynamics and that of the original system. The proposed method is based on the use of Haar Transform, particularly on its properties of approximating any function by a piecewise constant function and on its ability to concentrate energy in few coefficients in the transform domain. Numerical results presented here show the good performance of the proposed technique.