Embedding of nonlinear systems in a linear parameter-varying representation

Abstract

This paper introduces a systematic approach to synthesize linear parameter-varying (LPV) representations of nonlinear (NL) systems which are originally defined by control affine state-space representations. The conversion approach results in LPV state-space representations in the observable canonical form. Based on the relative degree concept of NL systems, the states of a given NL representation are transformed to new coordinates that provide its normal form. In the SISO case, all nonlinearities of the original system are embedded in one NL function which is factorized to construct the LPV form. An algorithms is proposed for this purpose. The resulting transformation yields an LPV model where the scheduling parameter depends on the derivatives of the inputs and outputs of the system. In addition, if the states of the NL model can be measured or estimated, then the procedure can be modified to provide LPV models scheduled by these states. Examples are included for illustration.