On unknown input observers designs for discrete-time LPV systems with bounded rates of parameter variation

Abstract

This paper concerns the design of a novel unknown input observer (UIO) for discrete-time linear parameter-varying (LPV) systems with bounded rates of parameter variation. The synthesis conditions have been formulated using a less conservative approach to obtain two different structures: a proportional UIO and a proportional-integral UIO. The main highlights of the present design conditions are the ability to deal with discrete-time LPV systems subject to both states and outputs parameter-varying matrices in the state-space representation and also the possibility of bounded rates of parameter variation. Such conditions may be useful to achieve better performance than considering only arbitrarily fast time-varying parameters for the discrete-time LPV representations. In order to obtain the UIO designs, stability and induced L2 norm performance conditions using a poly-quadratic approach in terms of Linear Matrix Inequalities are addressed. Numerical examples are presented to demonstrate the effectiveness of the proposed design methods.