An LMI approach to delay-dependent robust H<inf>∞</inf> filtering of lpv systems with discrete and distributed delays using PPDQ functions

This paper presents a delay-dependent approach to robust filtering for linear parameter-varying (LPV) systems with discrete and distributed time-invariant delays in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. Some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs) such that the filtering process remains asymptotically stable and satisfies a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level. Using polynomially parameter-dependent quadratic (PPDQ) functions and some Lagrange multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.