An LMI approach to H_∞ filtering for linear parameter-varying systems with delayed states and outputs

This paper considers the problem of delay-dependent robust H _∞ filtering for linear parameter-varying (LPV) systems with time-invariant delay in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. By taking the relation- ship between the terms in the Leibniz-Newton formula and a suitable change of variables into account, some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities so that the filtering process remains asymptotically stable and satisfies a prescribed H_∞ performance level. Using polynomially parameter-dependent quadratic functions and some multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust H _∞ filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.