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 relationship 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.