Delay-dependent parameter-dependent H∞ filtering for a class of LPV delayed systems using PPDQ functions

The problem of delay-dependent parameter-dependent H∞ filtering for state estimation of a class of LPV systems with multiple constant time delays in the state vector is investigated. With the help of polynomially parameter-dependent quadratic (PPDQ) functions and a suitable change of variables, the required sufficient conditions with high precision are established in terms of delay-dependent parameter-independent linear matrix inequalities (LMIs) for the existence of the desired H∞ filters. The explicit expression of the delay-dependent parameter-dependent H∞ filters is derived to satisfy both asymptotic stability and a prescribed level of disturbance attenuation. Accordingly, the designed filter will have the ability to track the plant states in the presence of external disturbances. Two numerical examples are provided to demonstrate the validity of the proposed design approach.

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