Discrete-time systems with linear parameter-varying: stability and H∞-filtering

In this paper, we investigate the problems of stability and H∞-filtering for a class of linear parameter-varying discrete-time (LPVDT) systems in which the state-space matrices depend affinely on time-varying parameters. We employ parameter-dependent Lyapunov functions to develop systematic procedures for testing the affine quadratic stability of the system. We develop a linear parameter-dependent filter such that the estimation error is affinely quadratically stable with a prescribed performance measure. It is shown that the solvability conditions can be expressed into linear matrix inequalities which are then evaluated at the vertices of the polytopic range of parameter values.  2002 Elsevier Science (USA). All rights reserved