Stability and H∞ filtering of linear parameter-varying discrete-time systems with state-delay

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 and has unknown constant state-delay. We employ the notion of affine quadratic stability using parameter-dependent Lyapunov functions and establish linear matrix inequality (LMI)-based procedures for testing the internal stability. Then, 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 LMIs which are then evaluated at the vertices of the polytopic range of parameter values.