Affine LPV Systems: Realization Theory, Input-Output Equations and Relationship with Linear Switched Systems

摘要

We formulate a Kalman-style realization theory for discrete-time affine LPV systems. By an affine LPV system we mean an LPV system whose matrices are affine functions of the scheduling parameter. In this paper we characterize those input-output behaviors which exactly correspond to affine LPV systems. In addition, we characterize minimal affine LPV systems which realize a given input-output behavior. Furthermore, we explain the relationship between Markovparameters, Hankel-matrices, existence of an affine LPV realization and minimality. The results are derived by reducing the problem to the realization problem for linear switched systems. In this way, as a secondary contribution, we formally demonstrate the close relationship between LPV systems and linear switched systems. In addition we show that and an input-output map has a realization by an affine LPV system if and only if it satisfies certain types of inputoutput equations.